complete unit 6 package - high school math teachers...unit 6 pacing chart highschoolmathteachers.com...

Complete Unit 6

Package

HighSchoolMathTeachers.com©2020

Table of Contents

Unit 6 Pacing Chart -------------------------------------------------------------------------------------------- 1

Geometry Unit 6 Skills List ---------------------------------------------------------------------------------------- 5

Unit 6 Lesson Plans -------------------------------------------------------------------------------------------- 6

Day 86 Bellringer -------------------------------------------------------------------------------------------- 42

Day 86 Activity -------------------------------------------------------------------------------------------- 44

Day 86 Practice -------------------------------------------------------------------------------------------- 47

Day 86 Exit Slip -------------------------------------------------------------------------------------------- 53

Day 87 Bellringer -------------------------------------------------------------------------------------------- 55

Day 87 Activity -------------------------------------------------------------------------------------------- 57

Day 87 Practice -------------------------------------------------------------------------------------------- 59

Day 87 Exit Slip -------------------------------------------------------------------------------------------- 62

Day 88 Bellringer -------------------------------------------------------------------------------------------- 64

Day 88 Activity -------------------------------------------------------------------------------------------- 66

Day 88 Practice -------------------------------------------------------------------------------------------- 68

Day 88 Exit Slip -------------------------------------------------------------------------------------------- 72

Day 89 Bellringer -------------------------------------------------------------------------------------------- 74

Day 89 Activity -------------------------------------------------------------------------------------------- 76

Day 89 Practice -------------------------------------------------------------------------------------------- 79

Day 89 Exit Slip -------------------------------------------------------------------------------------------- 84

Week 18 Assessment -------------------------------------------------------------------------------------------- 86

Day 91 Bellringer -------------------------------------------------------------------------------------------- 93

Day 91 Activity -------------------------------------------------------------------------------------------- 95

Day 91 Practice -------------------------------------------------------------------------------------------- 97

Day 91 Exit Slip -------------------------------------------------------------------------------------------- 101

Day 92 Bellringer -------------------------------------------------------------------------------------------- 103

Day 92 Activity -------------------------------------------------------------------------------------------- 105

Day 92 Practice -------------------------------------------------------------------------------------------- 108

Day 92 Exit Slip -------------------------------------------------------------------------------------------- 111

Day 93 Bellringer -------------------------------------------------------------------------------------------- 113

Day 93 Activity -------------------------------------------------------------------------------------------- 115

Day 93 Practice -------------------------------------------------------------------------------------------- 117

Day 93 Exit Slip -------------------------------------------------------------------------------------------- 122

Day 94 Bellringer -------------------------------------------------------------------------------------------- 124

Day 94 Activity -------------------------------------------------------------------------------------------- 126

Day 94 Practice -------------------------------------------------------------------------------------------- 129

Day 94 Exit Slip -------------------------------------------------------------------------------------------- 133

Week 19 Assessment -------------------------------------------------------------------------------------------- 135

Day 96 Bellringer -------------------------------------------------------------------------------------------- 142

Day 96 Activity -------------------------------------------------------------------------------------------- 144

Day 96 Practice -------------------------------------------------------------------------------------------- 146

Day 96 Exit Slip -------------------------------------------------------------------------------------------- 149

Day 97 Bellringer -------------------------------------------------------------------------------------------- 151

Day 97 Activity -------------------------------------------------------------------------------------------- 153

Day 97 Practice -------------------------------------------------------------------------------------------- 155

Day 97 Exit Slip -------------------------------------------------------------------------------------------- 161

Day 98 Bellringer -------------------------------------------------------------------------------------------- 163

Day 98 Activity -------------------------------------------------------------------------------------------- 165

Day 98 Practice -------------------------------------------------------------------------------------------- 167

Day 98 Exit Slip -------------------------------------------------------------------------------------------- 170

Day 99 Bellringer -------------------------------------------------------------------------------------------- 172

Day 99 Activity -------------------------------------------------------------------------------------------- 175

Day 99 Practice -------------------------------------------------------------------------------------------- 178

Day 99 Exit Slip -------------------------------------------------------------------------------------------- 183

Week 20 Assessment -------------------------------------------------------------------------------------------- 185

Day 101 Bellringer -------------------------------------------------------------------------------------------- 190

Day 101 Activity -------------------------------------------------------------------------------------------- 192

Day 101 Practice -------------------------------------------------------------------------------------------- 194

Day 101 Exit Slip -------------------------------------------------------------------------------------------- 198

Day 102 Bellringer -------------------------------------------------------------------------------------------- 200

Day 102 Activity -------------------------------------------------------------------------------------------- 202

Day 102 Practice -------------------------------------------------------------------------------------------- 205

Day 102 Exit Slip -------------------------------------------------------------------------------------------- 209

Day 103 Bellringer -------------------------------------------------------------------------------------------- 211

Day 103 Activity -------------------------------------------------------------------------------------------- 213

Day 103 Practice -------------------------------------------------------------------------------------------- 215

Day 103 Exit Slip -------------------------------------------------------------------------------------------- 218

Day 104 Bellringer -------------------------------------------------------------------------------------------- 221

Day 104 Activity -------------------------------------------------------------------------------------------- 223

Day 104 Practice -------------------------------------------------------------------------------------------- 225

Day 104 Exit Slip -------------------------------------------------------------------------------------------- 229

Week 21 Assessment -------------------------------------------------------------------------------------------- 231

Unit 6 Test -------------------------------------------------------------------------------------------- 236

Unit 6 Pacing Chart

HighSchoolMathTeachers.com ©2020 Page 1

Unit Week Day CCSS Standards Objective I Can Statements

Unit 6 Right

Triangle Relationships

and Trigonometry

Week 18 – Indirect

Measurements 86

CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right

triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for

acute angles.

Identify opposite, adjacent and hypotenuse of right

triangles. Define trigonometric ratios.

I can Identify opposite, adjacent and hypotenuse of

right triangles I can define trigonometric

ratios.

Unit 6 Right


and Trigonometry


Measurements 87



acute angles.

Find trigonometric ratios of angles

I can find trigonometric ratios of angles

Unit 6 Right


and Trigonometry


Measurements 88



acute angles.

Define trigonometric ratios of compliments.

I can define trigonometric ratios of compliments.

Unit 6 Right


and Trigonometry


Measurements 89



acute angles.

Use similarity to find the trigonometric ratios of triangles with common

angles.

I can use similarity to find the trigonometric ratios of

triangles with common angles.

Unit 6 Pacing Chart


Unit 6 Right


and Trigonometry


Measurements 90 Assessment Assessment Assessment

Unit 6 Right


and Trigonometry

Week 19 – Trigonometric

Ratios 91

CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine

and cosine of complementary angles.

Explain the relationship between sine and cosine of

complementary angles

I can explain the relationship between sine

and cosine of complementary angles

Unit 6 Right


and Trigonometry


Ratios 92

CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine

and cosine of complementary angles.

Use the relationship between the sine and cosine of complementary angles to

solve geometric problems

I can use the relationship between the sine and cosine of complementary angles to

solve geometric problems

Unit 6 Right


and Trigonometry


Ratios 93

CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in applied problems.*

Use trigonometric ratios to solve a triangle

I can use trigonometric ratios to solve a triangle

Unit 6 Right


and Trigonometry


Ratios 94

CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in applied problems.*

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in

word problems

I can use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in word problems

Unit 6 Pacing Chart


Unit 6 Right


and Trigonometry


Ratios 95 Assessment Assessment Assessment

Unit 6 Right


and Trigonometry

Week 20 – Special Right

Triangles 96



acute angles.

Find the trigonometric ratios of 30-60-90 right triangle

I can find the trigonometric ratios of 30-60-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 97



acute angles.

Solve 30-60-90 right triangle I can solve 30-60-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 98



acute angles.

Find the trigonometric ratios of 45-45-90 right triangle

I can find the trigonometric ratios of 45-45-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 99



acute angles.

Solve 45-45-90 right triangle I can solve 45-45-90 right

triangle

Unit 6 Pacing Chart


Unit 6 Right


and Trigonometry


Triangles 100 Assessment Assessment Assessment

Geometry Unit 6 Skills List Name ____________________________________

HighSchoolMathTeachers.com©2020 Page 5

Geometry Unit 6 Skills List

Number Unit CCSS Skill

24 6 HSG.SRT.C.6 Define trigonometric ratios for acute angles

25 6 HSG.SRT.C.7 Explain the relationship between the sine and cosine

of complementary angles

26 6 HSG.SRT.C.7 Use the relationship between the sine and cosine of

complementary angles

27 6 HSG.SRT.C.8 Solve right triangles in applied problems

28 6 HSG.SRT.D.9 Derive the formula A = 1/2ab sin(C) for the area of a

triangle

29 6 HSG.SRT.D.10 Prove the Laws of Sine’s and Cosines

30 6 HSG.SRT.D.10 Use the Laws of Sine’s and Cosines to solve problems

31 6 HSG.SRT.D.11

Apply the Law of Sine’s and the Law of Cosines to find

unknown measurements in right and non-right

triangles

Unit 6 Lesson Plan Name ____________________________________


Unit: Unit 6 Right Triangle Relationships and Trigonometry

Course: Geometry

Topic: Week 18 – Indirect Measurements

Day: 86

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively

Objective: Identify opposite, adjacent and hypotenuse of right triangles. Define trigonometric ratios.

I can statement: I can Identify opposite, adjacent and hypotenuse of right triangles I can define trigonometric ratios.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will identify the opposite side, the adjacent side and the hypotenuse of angles in a right triangle 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.

Materials: Bellringer 86 Day 86 Activities Day 86 Practice Day 86 Presentation Day 86 Exit Slip



Accommodations/Special Circumstances:

Technology:

Reflection:

Extra/Additional Resources:




Course: Geometry


Day: 87



Objective: Find trigonometric ratios of angles

I can statement: I can find trigonometric ratios of angles

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a right angle and verify the trigonometric ratios 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 88



Objective: Define trigonometric ratios of compliments.

I can statement: I can define trigonometric ratios of compliments.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least four to compare trigonometric ratios of two complementary angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 89


Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Objective: Use similarity to find the trigonometric ratios of triangles with common angles.

I can statement: I can use similarity to find the trigonometric ratios of triangles with common angles.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw similar triangles from a rectangle and find the trigonometric ratios of a common angle. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 90

Common Core State Standard: Assessment

Mathematical Practice: Assessment

Objective: Assessment

I can statement: Assessment

Procedures: Assessment

Materials: Assessment


Technology:

Reflection:





Course: Geometry

Topic: Week 19 – Trigonometric Ratios

Day: 91

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.

Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Objective: Explain the relationship between sine and cosine of complementary angles

I can statement: I can explain the relationship between sine and cosine of complementary angles

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a right angle and verify the equality of sine and cosine of complementary angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 92

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.

Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Objective: Use the relationship between the sine and cosine of complementary angles to solve geometric problems

I can statement: I can use the relationship between the sine and cosine of complementary angles to solve geometric problems

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 93

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Objective: Use trigonometric ratios to solve a triangle

I can statement: I can use trigonometric ratios to solve a triangle




Technology:



Reflection:





Course: Geometry


Day: 94

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Objective: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems

I can statement: I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems




Technology:



Reflection:





Course: Geometry


Day: 95








Technology:

Reflection:





Course: Geometry

Topic: Week 20 – Special Right Triangles

Day: 96


Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Objective: Find the trigonometric ratios of 30-60-90 right triangle

I can statement: I can find the trigonometric ratios of 30-60-90 right triangle




Technology:



Reflection:





Course: Geometry


Day: 97


Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Objective: Solve 30-60-90 right triangle

I can statement: I can solve 30-60-90 right triangle




Technology:



Reflection:





Course: Geometry


Day: 98



Objective: Find the trigonometric ratios of 45-45-90 right triangle

I can statement: I can find the trigonometric ratios of 45-45-90 right triangle




Technology:



Reflection:





Course: Geometry


Day: 99



Objective: Solve 45-45-90 right triangle

I can statement: I can solve 45-45-90 right triangle




Technology:



Reflection:





Course: Geometry


Day: 100








Technology:

Reflection:





Course: Geometry

Topic: Week 21 – Modeling with Right Triangles

Day: 101

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.


Objective: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

I can statement: I can derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.




Technology:



Reflection:





Course: Geometry


Day: 102

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.


Objective: Derive and apply sine rules

I can statement: I can derive and apply sine rules




Technology:



Reflection:





Course: Geometry


Day: 103

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.


Objective: Derive and apply cosine rules

I can statement: I can derive and apply cosine rules




Technology:



Reflection:





Course: Geometry


Day: 104

Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Objective: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

I can statement: I Understand and can apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).






Technology:

Reflection:


Day 86 Bellringer Name ____________________________________



Course: Geometry


Day: 105








Technology:

Reflection:




Use right ΔPQR (not drawn to scale) to answer the questions below.

1. Find the length QR.

2. Find the size of ∠QPR

3. Express the following length ratios in their simplest forms:

(a) PQ

QR

(b) PQ

PR

(c) QR

PR

P

Q R

14 in.

50 in.

16.3°



Answer keys

Day 86:

1. 48 in.

2. 73.7°

3. (a) 7

24

(b) 7

25

(c) 24

25

Day 86 Activity Name ____________________________________


1. Measure ∠X and fill its measure in the table provided.

2. Measure the measure the length of the hypotenuse and fill the length in the table provided below.

3. Measure the length of the side adjacent to ∠X and fill its length in the table under the column

labeled; length of the adjacent side. Note the position of the adjacent side with respect to ∠X.

X

Y Z



4. Measure the length of the side opposite to ∠X and fill in the table under the column labeled; length of

opposite side. Note the position of the opposite side with respect to ∠X.

5. Now use the measurements to determine the ratios of the indicated sides correct to two decimal

places, then fill in the three columns of the table.

6. Similarly, measure ∠Z and follow the steps 1-5 above to complete the second row of the table.

Table 1

Angle Angle measure

Length of hypotenuse

Length of adjacent side

Length of opposite side

Opposite side

Hypotenuse

Adjacent side

Hypotenuse

Opposite side

Adjacent side

∠𝑋

∠𝑍



In this activity students will work in groups of three to identify the opposite side, the adjacent side and

the hypotenuse of angles in a right triangle and to determine the ratios of these sides. Each of the

groups will be provided with a copy of ∆XYZ, a copy of table 1, a protractor and a ruler calibrated in

inches.

Answer keys Day 86:

1. Accuracy to be emphasized

2. Accuracy to be emphasized

3. Students should note that XY is adjacent to ∠X

4. Students should note that YZ is opposite to ∠X

5. The ratio 1.33 is written correct to two decimal places

6. Students should repeat the process, noting the adjacent and opposite sides in relation to ∠Z as they

did for ∠X

Table 1

Angle Angle measure

Length of hypotenuse

Length of adjacent side

Length of opposite side

Opposite side

Hypotenuse

Adjacent side

Hypotenuse

Opposite side

Adjacent side

∠𝑋 37° 5 in 4 in. 3 in. 0.6 0.8 0.75

∠𝑍 53° 5 in. 3 in. 4 in. 0.8 0.6 1.33

Day 86 Practice Name ____________________________________


Use right ∆𝐗𝐘𝐙 to answer question 1- 6 below.

Identify the following sides in relation to 𝛾.

1. The hypotenuse

2. The opposite side

3. The adjacent side

Use the sides of ∆XYZ to define the following trigonometric ratios, using 𝛾 as the reference angle:

4. tan 𝛾

5. cos 𝛾

6. sin 𝛾

X

Y Z

𝛾



Use right 𝚫𝐉𝐊𝐋 below to answer questions 7-12.

Name the following sides with reference to 𝜙.

7. opposite side

8. Adjacent side

9. Hypotenuse

Name the following sides with reference to 𝜏.

10. opposite side

11. Adjacent side

12. Hypotenuse

J

K

L

𝜙

𝜏



13. Sketch ΔPQR such that 𝜆 is the reference angle, PR is the opposite side, PQ is the adjacent side and

QR is the hypotenuse.

Study the figure below and use it to answer question 14 and 15.

If a person standing at point T glances up at the top of the building:

14. What name will be given to the side representing the distance from the person to the foot of the

building in relation to ΔTVS and ∠T?

15. What name will be given to the side representing the height of the building in relation to ΔTVS and

∠T?

16. Identify the hypotenuse from the figure above.

T

S

V

Bu

ildin

g



17. Show on the right ΔFGH the location of acute angle 𝛼 given that FG is the adjacent side.

The figure below shows the dimensions of a triangular pond represented as right 𝚫𝐁𝐂𝐃.

Use it to answer questions 18-20. All the dimensions are in feet.

State the lengths of the following sides with reference to ∠D:

18. The opposite side

19. The hypotenuse.

20. Calculate the length of the adjacent side.

F

H

G

B

D

C

841

840



Answer keys

Day 86:

1. XZ

2. XY

3. YZ

4. 𝑋𝑌

𝑌𝑍

5. 𝑌𝑍

𝑋𝑍

6. 𝑋𝑌

𝑋𝑍

7. KL

8. JK

9. JL

10. JK

11. KL

12. JL

13.

14. Adjacent side

15. opposite side

16. TS

P

R

Q

𝜆



17.

18. 840 ft.

19. 841 ft.

20. 41 ft.

F

H

G

𝛼

Day 86 Exit Slip Name ____________________________________


In ∆KLM identify the hypotenuse, the adjacent side and the opposite side for the marked acute angle 𝛼.

𝛼

K L

M



Answer keys Day 86:

KM is the hypotenuse

LM is the adjacent side

KL is the opposite side



Use the following diagram to answer the following questions

Identify the following from 1 - 3.

1. Adjacent side to 𝜏 and 𝛼.

2. Opposite side to 𝜏 and 𝛼.

3. Hypotenuse to 𝜏 and 𝛼.

4. Write the expressions for tan 𝜏 and sin 𝛼

5. Write the expressions for cos 𝛼 and sec 𝜏.

M N

T

𝜏

𝛼



Answer Keys

Day 87:

1. Adjacent side to 𝜏, 𝑀𝑇̅̅̅̅̅

Adjacent side to 𝛼 𝑀𝑁̅̅ ̅̅ ̅

2. Opposite side to 𝜏, 𝑀𝑁̅̅ ̅̅ ̅

Opposite side to 𝛼 𝑀𝑇̅̅̅̅̅

3. Hypotenuse side to 𝑁𝑇̅̅ ̅̅

4. tan 𝜏 =𝑀𝑁̅̅ ̅̅ ̅

𝑀𝑇̅̅ ̅̅̅

sin 𝛼 =𝑀𝑇̅̅̅̅̅

𝑁𝑇̅̅ ̅̅

5. cos 𝛼 =𝑀𝑁̅̅ ̅̅ ̅

𝑁𝑇̅̅ ̅̅

sec 𝜏 =𝑁𝑇̅̅ ̅̅

𝑀𝑇̅̅̅̅̅



1. Draw any right angle triangle and label it as shown below.

2. Measure segments 𝐷𝐸̅̅ ̅̅ , 𝐸𝐹̅̅ ̅̅ and 𝐹𝐷̅̅ ̅̅ .

3. Measure the following angles ∠𝐷 and ∠𝐹

4. Use measurements in 2 above to find sine, cosine, and tangent of ∠𝐷 and ∠𝐹.

5. Use measurements in 3 above to find sine, cosine, and tangent of ∠𝐷 and ∠𝐹.

6. Compare the similar ratios of the same angles in 4 and 5 above.

D E

F



In this activity, students will draw a right angle and verify the trigonometric ratios. Each group will be

composed of at least 3 students and will require a protractor, a ruler, a pencil and a plane paper.

Answer Keys

Day 87:

1. No response

2. Different responses but must satisfy the Pythagorean Theorem.

3. Different responses but must add up to 90°.

4 - 5. Different responses

6. Similar ratios of the same angles



Use the following information to answer questions 1 – 11

Find the following ratios

1. cos𝛼

2. sin 𝛼

3. tan 𝛼

4. cos𝜃

5. sin 𝜃

6. tan 𝜃

7. sec 𝜃

8. cot 𝜃

9. cot 𝛼

10. csc 𝜃

11. sec 𝛼

G H

J

𝛼

𝜃

6 in

16 in

17.08 in



Use the following information to answer questions 12 - 18

Find the following trigonometric ratios

12. tan ∠𝐻

13. cos 𝛼

14. sin 𝛼

15. tan 𝛼

16. sin ∠𝐻

17. cot ∠𝐻

18. sec ∠𝐻

19. Find the tangent and sine of 90°

20. Find the tangent and sine of 80°

G H

J

𝛼

48°



Answer keys

Day 87:

1. 0.3513

2. 0.9368

3. 2.667

4. 0.9368

5. 0.3513

6. 0.375

7. 1.068

8. 2.667

9. 0.375

10. 2.847

11. 2.847

12. 1.111

13. 0.7431

14. 0.6691

15. 0.9004

16. 0.7431

17. 0.9004

18. 1.494

19. tan 90° 𝑖𝑠 𝑛𝑜𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑

sin 90° = 1

20. tan 80° = 5.671

sin 80° = 0.9848



The opposite and adjacent side of an angle in a right triangle is 12 in and 9 in respectively. Find the

cosine, tangent and cosecant of the angle.



Answer Keys

Day 87

Let the angle be 𝑥

cos 𝑥 = 0.6

tan 𝑥 = 1.333

csc 𝑥 = 1.25



1. Find the complements of the following angles.

(a) 11°

(b) 89°

(c) 𝜃

2. In right ∆PQR below ∠QPR = 𝛼. Use it to answer the questions that follow.

(a) Find the measure of ∠PRQ in terms of 𝛼.

(b) Identify the side adjacent to ∠PRQ

(c) Identify the side opposite to ∠PRQ

R

Q P

𝛼



Answer keys

Day 88:

1. (a) 79°

(b) 1°

(c) 90° − 𝜃

2. (a) 90° − 𝛼

(b) QR

(c) PQ



1. Measure ∠𝐹 and write down its measure.

2. Measure ∠𝐻 and write down its measure.

3. Find the sum of ∠𝐹 and ∠𝐻. What is the name given to such a pair of angles?

4. Express the sine, cosine and tangent of ∠𝐹 in terms of 𝑓, 𝑔 and ℎ where applicable.

5. Express the sine, cosine and tangent of ∠𝐻 in terms of 𝑓, 𝑔 and ℎ where applicable.

6. Compare the expressions for the sines, cosines and tangents of the two angles. State whether the

expressions are similar or different for each trigonometric ratio of the each of the two angles.

F

G H

𝑔 ℎ

𝑓



In this activity, students will work in groups of four to compare trigonometric ratios of two

complementary angles. The students in the groups will be equipped with a protractor, and a copy of

right ∆FGH labeled such that ∠𝐺 is the right angle, ∠𝐹 = 30° and ∠𝐻 = 60°. The sides should be

labelled as shown.

Answer keys

Day 88:

1. ∠𝐹 = 30°

2. ∠𝐻 = 60°

3. The sum is 90°; Complementary angles

4. sin 𝐹 =𝑓

𝑔

cos 𝐹 =ℎ

𝑔

tan 𝐹 =𝑓

ℎ

5. sin 𝐻 =ℎ

𝑔

cos 𝐻 =𝑓

𝑔

tan 𝐻 =ℎ

𝑓

6. The expressions are different for each trigonometric ratio of each angle.



Use right ∆𝐉𝐊𝐋 below to answer questions 1-8.

1. Find the sum 𝛼 + 𝛽.

2. What is the name was given to the pair of angles 𝛼 and 𝛽 from your sum in question 1 above?

Express the following trigonometric ratios of 𝜶 in terms of 𝒋, 𝒌 and 𝒍 where applicable.

3. sin 𝛼

4. cos 𝛼

5. tan 𝛼

Similarly, express the following trigonometric ratios of 𝜷 in terms of 𝒋, 𝒌 and 𝒍 where applicable.

6. sin 𝛽

7. cos 𝛽

8. tan 𝛽

J

K L

𝑘

𝑙

𝑗

𝛽

𝛼



Use right ∆𝐑𝐒𝐓 below to answer questions 9-16.

9. Write ∠𝑇 in terms of 𝜏

10. What is the sum of ∠𝑅 and ∠𝑇?

Express the following trigonometric ratios of ∠𝑅 in terms of 𝑟, 𝑠 and 𝑡 where applicable.

11. sin 𝑅

12. cos 𝑅

13. tan 𝑅

Express the following trigonometric ratios of ∠𝑇 in terms of 𝑟, 𝑠 and 𝑡 where applicable.

14. sin 𝑇

15. cos 𝑇

16. tan 𝑇

R

S T

𝑠

𝑡

𝑟

𝜏



In right ∆𝐌𝐍𝐏 below ∠𝑷 = 𝟗𝟎° − 𝜽. Use it to answer questions 17-20.

17. Write ∠𝑀 in terms of 𝜃.

18. Write an expression as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the sine of 90° − 𝜃

19. Write an expression as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the cosine of 90° −

𝜃

20. Write an expression in as a ratio in terms of 𝑚, 𝑛 and 𝑝 where applicable to show the tangent of

90° − 𝜃

M

N P

𝑛

𝑝

𝑚

90° − 𝜃



Answer keys

Day 88:

1. 90°

2. 𝛼 and 𝛽 are complements to each other/

they are complementary angles

3. sin 𝛼 =𝑙

𝑘

4. cos 𝛼 =𝑗

𝑘

5. tan 𝛼 =𝑙

𝑗

6. sin 𝛽 =𝑗

𝑘

7. cos 𝛽 =𝑙

𝑘

8. tan 𝛽 =𝑗

𝑙

9. 90° − 𝜏

10. 90°

11. sin 𝑅 =𝑟

𝑠

12. cos 𝑅 =𝑡

𝑠

13. tan 𝑅 =𝑟

𝑡

14. sin 𝑇 =𝑡

𝑠

15. sin 𝑇 =𝑟

𝑠

16. tan 𝑇 =𝑡

𝑟

17. 𝜃

18. sin(90° − 𝜃) =𝑝

𝑛

19. cos(90° − 𝜃) =𝑚

𝑛

20. tan(90° − 𝜃) =𝑝

𝑚



Use right ∆KLM to answer the questions that follow.

(a) Find the sum 𝛼 + (90° − 𝛼).

(b) Express the sine of (90° − 𝛼) in terms of 𝑘 and 𝑙.

(c) Express the cosine of (90° − 𝛼) in terms of 𝑚 and 𝑙.

K

L M

𝑙

𝑚

𝑘

90° − 𝛼

𝛼



Answer keys

Day 88:

(a) 90°

(b) 𝑘

𝑙

(c) 𝑚

𝑙



1.Use the figure below to answer the questions that follow.

a) Calculate sin 𝜃

b) Calculate cos 𝜃

c) Calculate tan 𝜃

d) Calculate cos 𝛼

2. Which angle is shared by ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐶?

A B

C

D E

𝛼

𝜃

6 𝑖𝑛 3 𝑖𝑛

5.2 𝑖𝑛



Answer Key Day 89:

1. a) 0.5

b) 0.867

c) 0.577

d) 0.5

2. ∠𝐶



1. Construct a rectangle measuring 3 𝑖𝑛 by 4 𝑖𝑛 on a plane paper and label it ABCD such that the longer

sides are AB and CD as shown.

2. Measure 1 𝑖𝑛 from A along side AD and label it E.

3. Measure 1 𝑖𝑛 from A along side BC and label it F.

4. Draw a diagonal to join A and C and label its intersection point with line EF as G.

5. Which angle is common in ∆𝐴𝐷𝐶 and ∆𝐴𝐷𝐺?

6. Measure the lengths of sides in the first row of the table below and record them in the second row.

AD DC AC AE EG GA

A B

D C



7. Find the trigonometric ratios of ∠𝐶𝐴𝐷 and ∠𝐺𝐴𝐸 and record your results in the following table. Write

your answer in one decimal place.

∠𝐶𝐴𝐷 ∠𝐺𝐴𝐸

sin

cos

tan



In this activity, students will draw similar triangles from a rectangle and find the trigonometric ratios of a

common angle. Students will work in groups of at least three and each group is required to have a ruler,

a protractor a pencil and a plain paper.

Answer Keys Day 89:

1-4. No response

5. ∠𝐴

6.

AD DC AC AE EG GA

𝟑 𝒊𝒏 4 𝑖𝑛 5 𝑖𝑛 1 𝑖𝑛 1.3 𝑖𝑛 1.7 𝑖𝑛

7.

∠𝐶𝐴𝐷 ∠𝐺𝐴𝐸

sin 0.8 0.8

cos 0.6 0.6

tan 1.3 1.7



Use the figure below to answer questions 1-6.

Leave your answer in fraction form.

.

1. Calculate the cosine of ∠𝑆𝑇𝑈.

2. Calculate the cosine of ∠𝑀𝑇𝑁.

3. Calculate the sine of ∠𝑆𝑇𝑈.

4. Calculate the sine of ∠𝑀𝑇𝑁

5. Calculate the tangent of ∠𝑆𝑇𝑈

6. Calculate the tangent of ∠𝑀𝑇𝑁

S M T

U

N

60 𝑖𝑛 120 𝑖𝑛

33 𝑖𝑛

61 𝑖𝑛

122 𝑖𝑛

22 𝑖𝑛



Use the diagram below to answer questions 7-12.

7. Calculate the sine of ∠𝐴𝐿𝐵.

8. Calculate the sine of ∠𝐽𝐿𝐾.

9. Calculate the cosine of ∠𝐴𝐿𝐵.

10. Calculate the cosine of ∠𝐽𝐿𝐾.

11. Calculate the tangent of ∠𝐴𝐿𝐵.

12. Calculate the sine of ∠𝐽𝐿𝐾.

J

K

L

A

B


8 𝑖𝑛

6 𝑖𝑛

10 𝑖𝑛

10 𝑖𝑛



Use the diagram below to answer questions 13-18

13. Calculate the sine of ∠𝐽𝐶𝐾.

14. Calculate the sine of ∠𝐴𝐶𝐵.

15. Calculate the cosine of ∠𝐽𝐶𝐾.

16. Calculate the cosine of ∠𝐴𝐶𝐵.

17. Calculate the tangent of ∠𝐴𝐶𝐵.

18. Calculate the tangent of ∠𝐽𝐶𝐾

A

B

C

J

K

20 𝑖𝑛 63 𝑖𝑛

40 𝑖𝑛

58 𝑖𝑛

29 𝑖𝑛

21 𝑖𝑛



Use the diagram below to answer questions 19 and 20

19. Calculate the cosine of ∠𝑇𝑅𝑈.

20. Calculate the cosine of ∠𝑄𝑅𝑆.

Q R

S

T

U


24 𝑖𝑛 13 𝑖𝑛

13 𝑖𝑛



Answer Keys

Day 89:

1. 60

61

2. 60

61

3. 11

61

4. 11

61

5. 11

60

6. 11

60

7. 3

5

8. 3

5

9. 4

5

10. 4

5

11. 3

4

12. 3

4

13. 21

29

14. 21

29

15. 20

29

16. 20

29

17. 21

20

18. 21

20

19. 5

13

20. 5

13



In the diagram below, 𝐶𝑇 = 3 𝑖𝑛 and 𝑆𝑇 = 3.6 𝑖𝑛.

Calculate the tangent of ∠𝐴𝐶𝐵

A B

C

S T



Answer Keys Day 89:

1. 1.2

86

High School Math Teachers

Geometry

Weekly Assessment Package

Week 18

©2020HighSchoolMathTeachers

87

Week 18

Weekly Assessment

88

Week #18

1. The following images are similar.

a). Find the length of NL and NM b). What would the distance around NL?

2. a).Identify the reason that makes the two triangles similar.

b). Then find the value of the third angle

2 in 9 in

6 in

6.5 in

L

M

N

20°

20°

115°

115°

89

3. Use the diagram below to answer the

questions

a). Identify the opposite and adjacent sides to 𝛼

b). Express the sine and tangent of 𝛼 in terms of the sides of the triangle

4. Use postulates of congruence and similarity to

show that triangle ABC and ACD are congruent if

ABCD is a rectangle.

5. Find the trigonometric ratios of 30°, 25° and

68° 6. Given that sin 𝜃 =

1

3

a). Find 𝑐𝑜𝑠 𝜃 and tan 𝜃 (give the exact answer)

b). Find sin(90° − 𝜃)

N M

P

𝛼

A B

C D

90

Week 18 - KEYS

Weekly Assessments

91

Week #18 KEY 1. The following images are similar.

a). Find the length of NL and NM 27 in b). What would the distance around NL? 29.25 in

2. a).Identify the reason that makes the two triangles similar.

AA criterion b). Then find the value of the third angle 45°

2 in 9 in

6 in

6.5 in

L

M

N

20°

20°

115°

115°

92

3. Use the diagram below to answer the

questions

a). Identify the opposite and adjacent sides to 𝛼 Opposite side is NM Adjacent side is PN b). Express the sine and tangent of 𝛼 in terms of the sides of the triangle

sin 𝛼 =𝑁𝑀

𝑃𝑀; tan 𝛼 =

𝑁𝑀

𝑃𝑁

4. Use postulates of congruence and similarity to

show that triangle ABC and ACD are congruent if

ABCD is a rectangle.

𝐴𝐶 is common to both triangles 𝐴𝐵 = 𝐶𝐷 (Opposite sides of a rectangle) 𝐴𝐷 = 𝐶𝐵 (Opposite sides of a rectangle) Since corresponding sides are equal, we have the postulate SSS hence the two triangles are congruent

5. Find the basic trigonometric ratios of 30°and

68°

tan 30° = 0.5774, sin 30° = 0.5, cos 30° = 0.866 tan 68° = 0.3746, sin 68° = 0.9271, cos 68° = 0.3746

6. Given that sin 𝜃 =1

3

a). Find 𝑐𝑜𝑠 𝜃 and tan 𝜃 (give the exact answer)

cos 𝜃 =2√2

3, tan 𝜃 =

1

2√2

b). Find sin(90° − 𝜃)

sin 𝜃 =2√2

3

N M

P

𝛼

A B

C D



Use the following diagram to answer the following questions.

𝑇𝐵̅̅ ̅̅ = 17 𝑖𝑛, 𝑇𝐾̅̅ ̅̅ = 9 𝑖𝑛 .

1. Find the size of angle KTB in terms of 𝑟.

2. Find the length of 𝐾𝐵̅̅ ̅̅ .

3. Find tan 𝑟

4. Find cos ∠𝑇

5. Find csc 𝑟.

K T

B

𝑟



Answer Keys

Day 91:

1. 90 − 𝑟

2. 14.42 𝑖𝑛

3. 0.6241

4. 0.5294

5. 1.889



1. Draw any right angle triangle and label it as shown below.

2. Measure segments 𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ and 𝐶𝐴̅̅̅̅ .

3. Measure the following angles ∠𝐴 and ∠𝐶

4. Find the sum of the angles in 3 above.

5. Use measurements in 2 above to find sine, cosine of ∠𝐷 and ∠𝐹.

6. Use measurements in 3 above to find sine, cosine of ∠𝐷 and ∠𝐹.

7. Compare the sine and cosine of ∠𝐷 and ∠𝐹 respectively

8. Compare the cosine and sine of ∠𝐷 and ∠𝐹 respectively

A B

C



In this activity, students will draw a right angle and verify the equality of sine and cosine of

complementary angles. Each group will be composed of at least 3 students and will require a protractor,

a ruler, a pencil and a plain paper.

Answer Keys

Day 91:

1 No response

2. Different responses but must satisfy the Pythagorean theorem

3. Different responses but must add up to 90°.

4. They add up to 90°

5 - 6. Different responses

7. They are equal

8. They are equal



Use the following information to answer questions 1 – 15

In the figure above, ABCD is a rectangle measuring 24 in by 10 in.

1.Find the length of AC.

2. Find cos ∠𝐵𝐴𝐶

3. Find cos ∠𝐴𝐶𝐵

4. Find sin ∠𝐵𝐴𝐶

5. Find sin ∠𝐴𝐶𝐵

6. Compare your answer in 2 and 5 above. What do you notice?


A B

C D



8. Find cos ∠𝐷𝐴𝐶

9. Find cos ∠𝐷𝐶𝐴

10. Find sin ∠𝐷𝐴𝐶

11. Find sin ∠𝐷𝐶𝐴



14. Identify a common feature that the angles whose ratios are being compared in 13 and 12 above

have?

15. What is your conclusion from the relations in 12, 13 and 14 above?



Use the following information to answer questions 16 - 20

16. Find cos ∠𝑌

17. Find cos ∠𝑆

18. Find sin ∠𝑆

19. Find sin ∠𝑌

20. Compare your answers in 16 and 19 above and explain your answer.

T Y

S

56°



Answer keys

Day 91:

1. 26 in

2. 0.9231

3. 0.3846

4. 0.3846

5. 0.9231

6. They are equal

7. They are equal

8. 0.3846

9. 0.9231

10. 0.9231

11. 0.3846

12. They are equal

13. They are equal

14. They add up to 90°

15. Sine and cosine of two complementary angles are equal

16. 0.5592

17. 0.8290

18. 0.5592

19. 0.8290

20. They are equal



Find the sine and cosine of 𝛼 and 𝜃 respectively hence compare the answers.

𝜃

𝛼

9 𝑖𝑛

25 𝑖𝑛



Answer Keys

Day 91

sin 𝛼 = 0.96

cos 𝜃 = 0.96

They are equal



In right ∆PQR below, the measure of ∠P is given as 𝛼 and that of ∠R by 𝛽. Use it to determine the

following values:

(a) sin 𝛼

(b) cos 𝛼

(c) sin 𝛽

(d) cos 𝛽

(e) 𝛼 + 𝛽

Using the values above, identify one trigonometric ratio that is equal to:

(f) sin 𝛼

(g) cos 𝛼

R

P L 𝑐

𝑎

𝑏

𝛽

𝛼



Answer keys:

Day 92:

(a) sin 𝛼 =𝑏

𝑎

(b) cos 𝛼 =𝑐

𝑎

(c) sin 𝛽 =𝑐

𝑎

(d) cos 𝛽 =𝑏

𝑎

(e) 90°

(f) cos 𝛽

(g) sin 𝛽



1. Use the sine and cosine tables you have been provided with to find the sine and cosine of the

tabulated angles.

2. List all pairs of complementary angles from the tabulated angles above.

3. What do you notice about sin 10° and cos 80° from your values in the table above?

4. What do you notice about cos 10° and sin 80° from your values in the table above?

5. What do you notice about sin 20° and cos 70° from your values in the table above?

6. What do you notice about cos 70° and sin 20° from your values in the table above?

Angle Sine Cosine

10°

20°

30°

40°

50°

60°

70°

80°



7. Compare the sine of one angle to the cosine of the other angle in each of the pairs of complementary

angles you have listed in 2 above. What do you notice?

8. Now, compare the cosine of one angle to the sine of the other angle in each of the pairs of

complementary angles you have listed in 2 above. What do you notice?

9. Try the process in 7 and 8 above for any two pairs of complementary angles of your choice. What

does this tell you about the sine and cosine of any pair of complementary angles?



In this activity, students will work in groups of four to deduce the relationship between sine and cosine

of complementary angles using trigonometrical tables. The students should be equipped with

trigonometrical tables having sine and cosine tables. Note the values in the tables are given correctly to

four significant figures.

Answer keys Day 92:

1.

2. 10° and 80°

20° and 70°

30° and 60°

40° and 50°

3. sin 10° = cos 80°

4. cos 10° = sin 80°

5. sin 20° = cos 70°

6. cos 70° = sin 20°

7. The sine of one angle is equal to the cosine of the other angle in each pair

8. The cosine of one angle is equal to the sine of the other angle in each pair

9. The cosine of any angle is equal to the sine of its complement and the sine of any angle is equal to the

cosine of its complement.

Angle Sine Cosine

10° 0.7136 0.9848

20° 0.3420 0.9397

30° 0.5000 0.8660

40° 0.6428 0.7660

50° 0.7660 0.6428

60° 0.8660 0.5000

70° 0.9397 0.3420

80° 0.9848 0.7136



Given that the pair of angles is acute, find the value of 𝜽 in questions 1-5.

1. cos 11° = sin 𝜃

2. sin 58° = cos 𝜃

3. cos(2𝜃 + 16°) = sin 2𝜃

4. sin(𝜃 − 36°) = cos 𝜃

5. cos 2𝜃 = sin(𝜃 + 18°)

6. In right ∆KLM, ∠L is the right angle and sin 𝑀 = 𝜃. What will be the value of cos ∠𝐾?

7. In right ∆PQR, ∠Q is the right angle and cos 𝑃 = 𝛼. What will be the value of sin 𝑅?

8. Given that sin(2𝑥 + 20°) = cos(𝑥 + 40°), find the measures of the two acute angles in the

corresponding right triangle.

9. In right ∆XYZ, ∠Y is the right angle and cos 𝑋 = 4𝑥 − 9 and sin 𝑍 = 3𝑥 − 6. Calculate the value of 𝑥.

10. In right ∆JKL, ∠K is the right angle and cos 𝐽 = 𝑥 and sin 𝐽 = 𝑦. Write an expression for

sin 𝐿 + cos 𝐿.



11. Identify an angle measure where the sine and cosine have the same value.

12. Given that sin 60° =√3

2 and cos 𝛼 =

√3

2. Find 𝛼.

13. Given that sin 66° = 0.9135, find the cosine of the complementary angle.

14. Given that cos 23° = 0.9205, find the sine of the complementary angle.

In questions 15-20, solve for the unknown.

15. sin (5

2𝑦 + 12°) = cos (

1

2𝑦)

16. cos(7𝑧 + 15°) = sin(3𝑧 + 40°)

17. sin 𝑘 = cos 2𝑘

18. cos (1

3𝑛 + 2°) = sin 43°

19. sin(2𝑝 + 1°) = cos 44°

20. cos(5𝑥 + 10°) = sin(4𝑥 − 19°)



Answer keys

Day 92:

1. 79°

2. 32°

3. 18.5°

4. 63°

5. 24°

6. 𝜃

7. 𝛼

8. 40° and 50°

9. 𝑥 = 3

10. 𝑥 + 𝑦

11. 45°

12. 30°

13. 0.9135

14. 0.9205

15. 𝑦 = 26°

16. 𝑧 = 3.5°

17. 𝑘 = 30°

18. 𝑛 = 135°

19. 𝑝 = 22.5°

20. 𝑥 = 11°



Solve for 𝛼 in the following equations given that the angles are acute.

(a) sin(𝛼 − 54°) = cos 𝛼

(b) cos(𝛼 + 42°) = sin 2𝛼



Answer keys

Day 92:

(a) 𝛼 = 72°

(b) 𝛼 = 16°



1. Use the figure below to answer the questions that follow.

a) Use Pythagorean theorem to find the length of the side labeled 𝑏.

b) Calculate sin 30°

c) Calculate cos 30°

d) Calculate sin 60°

e) Calculate cos 60°

30°

60°

10 𝑖𝑛

20 𝑖𝑛

𝑏



Answer Key Day 93:

1. a) 17.32 𝑖𝑛

b) 0.5

c) 0.866

d) 0.866

e) 0.5



In this activity, students will draw a right triangle and solve it using the trigonometric ratios. Students

will work in groups of at least three and each group is required to have a pencil, a ruler, a plain paper

and a compass.

1. Draw a line which is 4 𝑖𝑛 long and label it AB.

2. Construct a line perpendicular to AB passing through end A.

3. Construct a line making an angle of 60° with AB at point B and extend it to intersect with line

perpendicular to AB at point C.

4. Using trigonometric ratios, calculate the lengths of line AC and BC.

What are their lengths?

5. Using a ruler measure the length of line AC and BC.

What do you get? Are they equal to the results you got in step 4 above?



Answer Keys

Day 93:

1-3. No response

4. AC is about 7 𝑖𝑛

BC is about 8 𝑖𝑛

5. AC is about 7 𝑖𝑛

BC is about 8 𝑖𝑛

Yes



Use the figure below to answer questions 1-2.

1. Find the length of AB.

2. Find the length of BC.

Use the figure below to answer questions 3-4

3. Find the value of a.

4. Find the value of b.

A B

C

2 𝑖𝑛

45°

5 𝑖𝑛

20°

a

b



Use the diagram below to answer questions 5 and 6.

5. Find the value of c.

6. Find the value of d

Use the figure below to answer questions 7-12

𝑆𝑈 = 20 𝑖𝑛 and ∠𝑈𝑆𝑉 = 50°.

7. Find the length of ST.

8. Find the length of UV.

9. Find the size of angle T.

39°

15 𝑖𝑛

d

c



10. Calculate the length of SV

11. Calculate the length of UT.

12. Calculate the size of VT

Use the figure below to answer questions 13 to 18.

13. Find the length of MJ.

14. Find the length of JL.

15. Find the size of ∠𝐾.

16. Find the length of JK.

12 𝑖𝑛 20 𝑖𝑛 40°

K L

M

J



Use the figure below to answer questions 17 and 18.

17. Find the value of 𝑥

18. Find the value of 𝑦

19. Find the size of ∠𝑁

20. Find the value of 𝜃

75°

𝑥

𝑦

25 𝑖𝑛

M N

O


S T

U

18 𝑖𝑛

14 𝑖𝑛



Answer Key Day 93:

1. 2 𝑖𝑛

2. 2.83 𝑖𝑛

3. 13.74 𝑖𝑛

4. 14.62 𝑖𝑛

5. 18.52 𝑖𝑛

6. 23.84 𝑖𝑛

7. 31.1 𝑖𝑛

8. 15.3 𝑖𝑛

9. 40°

10. 12.8 𝑖𝑛

11. 23.8 𝑖𝑛

12. 18.3 𝑖𝑛

13. 26.11 𝑖𝑛

14. 16.8 𝑖𝑛

15. 54.4°

16. 20.63 𝑖𝑛

17. 6.47 𝑖𝑛

18. 24.15 𝑖𝑛

19. 51°

20. 38.9°



1. Use trigonometric ratios to find the value of 𝑥 in the figure below.

𝑥

30°

8 𝑖𝑛



Answer Keys Day 93:

1. 4 𝑖𝑛



In right ∆ABC below ∠C = 31° and AD = 24 𝑖𝑛. The figure is not drawn to scale and all lengths are in

inches.

(a) Find the measure of ∠A.

Calculate the length of the following sides, giving your answers correct to two decimal places.

(b) AB

(c) BD

(d) BC

(e) DC

A

B C

D

31°

24 𝑖𝑛.



Answer keys

Day 94:

(a) ∠A = 59°

(b) 46.60 𝑖𝑛.

(c) 39.94 𝑖𝑛.

(d) 77.56 𝑖𝑛.

(e) 66.48 𝑖𝑛.



1. Measure the length of the wooden pole using the surveyor’s tape measure provided.

2. Record the length of the pole in the writing pad provided.

3. Let one member of your group hold the pole upright ensuring that the flat surface is properly aligned

to the ground.

4. Measure the length of the shadow formed by the pole using the tape measure.

5. Record the length of this shadow in the writing pad provided.

6. Record the time at the moment you are measuring the length of the shadow.

7. The sketch below represents a right triangle to depict

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