fg10101...2 2 m 15 m d tan d 9. 5 5 ft 3 ft d tan d 10. 7 yd 15 yd f tan f 11. 2 6 yd 6 yd f tan f...

Chapter 12 ● Skills Practice 471

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Skills Practice Skills Practice for Lesson 12.1

Name _____________________________________________ Date _________________________

Wheelchair RampsThe Tangent Ratio

Vocabulary Define each term in your own words.

1. tangent of an angle

Problem Set Calculate the tangent of each angle. Rationalize the denominator when necessary.

2.

3 ft

4 ftA

tan A �

3.

8 ft

6 ft

A

tan A �

4. 2 ft

2 ft

B

tan B �

5.

3 2 ft

3 2 ft

B

tan B �

6.

25 m

20 mC

tan C �

7.

40 m

32 m

C

tan C �

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472 Chapter 12 ● Skills Practice

12

8.

2 2 m

15 mD

tan D �

9.

5 5 ft

3 ft

D

tan D �

10.

7 yd

15 yd

F

tan F �

11.

2 6 yd

6 yd

F

tan F �

Use a calculator to evaluate each tangent ratio. Round your answers to the nearest hundredth.

12. tan 30° 13. tan 45°

14. tan 60° 15. tan 15°

16. tan 90° 17. tan 180°


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Name _____________________________________________ Date _________________________

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Calculate the missing length of each triangle. Round your answers to the nearest hundredth.

18.

x

2 ft

40°

19. x

6 ft

60°

20.

15 m

x

20°

21.

2 m

x

5°

22.

25°

11 yd

x 23.

63°

3 2 yd

x

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Use a tangent ratio to solve each problem. Round your answers to the nearest hundredth.

24. A boat travels in the following path. How far north did it travel?

25. During a group hike, a park ranger makes the following path. How far west did they travel?

26. A surveyor makes the following diagram of a hill. What is the height of the hill?

27. To find the height of a tree, a botanist makes the following diagram. What is the height of

the tree?

23°

45 miles

N

N12°

2 miles

35°

2450 ft

70°

20 ft


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Name _____________________________________________ Date _________________________

Golf Club DesignThe Sine Ratio

Vocabulary Given the triangle below, write each of the following trigonometric ratios of angle A.

zy

xA

1. sine of an angle

2. tangent of an angle

Problem Set Calculate the sine of each angle. Rationalize the denominator when necessary.

3.

8 ft12 ft

A

sin A �

4.

2 ft

A

2 2 ft

sin A �

5.

6 ft

B

3 3 ft

sin B �

6. 7 ft

14 ft

B

sin B �

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7.

25 m35 m

C

sin C �

8.

2 2 m

15 m

C

sin C �

9.

3 m

D

36 3 m

sin D �

10.

54 m

D

6 3 m

sin D �

11.

25 yd

15 yd

F

20 yd

sin F �

12.

12 yd

F

6 3 yd

6 yd

sin F �


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Name _____________________________________________ Date _________________________

12

Use a calculator to evaluate each sine ratio. Round your answers to the nearest hundredth.

13. sin 30° 14. sin 45°

15. sin 60° 16. sin 15°

17. sin 90° 18. sin 180°


19.

x2 ft

40° 20.

x

6 ft60°

21.

15 mx

20°

22.

2 m

x

5°

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23.

25°

11 yd

x

24. 63°

3 2 mx

Use a sine ratio to solve each problem. Round your answers to the nearest hundredth.

25. A scout troop traveled 12 miles from camp, as shown on the map below. How far north did

they travel?

26. An ornithologist tracked a Cooper’s hawk that traveled 23 miles. How far east did the bird

travel?

27. An architect needs to use a diagonal support in an arch. Her company drew the following

diagram. How long does the diagonal support have to be?

18°

12 miles

N

N

15°

23 miles

35°

12 ft


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Name _____________________________________________ Date _________________________

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28. A hot air balloon lifts 125 feet into the air. The diagram below shows that the hot air balloon

was blown to the side. How long is the piece of rope that connects the balloon to the

ground?

9°

125 ft

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Name _____________________________________________ Date _________________________

Attaching a Guy WireThe Cosine Ratio

VocabularyWrite the term from the box that best completes the statement.

cosine of an angle trigonometric ratio sine of an angle tangent of an angle

1. The is the ratio of the length of the opposite side of the angle of a

right triangle, to the length of the hypotenuse.

2. A is a ratio of two sides of a right triangle.

3. The is the ratio of the length of the adjacent side of the angle of a

right triangle, to the length of the hypotenuse.

4. The is the ratio of the length of the opposite side of the angle of a

right triangle, to the adjacent side of the angle.

Problem Set Calculate the cosine of each angle. Rationalize the denominator when necessary.

5.

8 ft

12 ft

A

cos A �

6.

2 ft

A

2 2 ft

cos A �

7.

6 ft

B3 3 ft

cos B �

8.

7 ft

14 ft

B

cos B �

9.

25 m 35 m

C

cos C �

10.

2 2 m

15 m

C

cos C �

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11.

3 m

D

36 3 m

cos D �

12.

54 m

D6 3 m

cos D �


13.

25 yd

15 yd

F

20 yd

cos F �

14.

12 yd

F

6 3 yd

6 yd

cos F �

Use a calculator to evaluate each cosine ratio. Round your answers to the nearest hundredth.

15. cos 30° 16. cos 45°

17. cos 60° 18. cos 15°

19. cos 90° 20. cos 180°

21.

x

2 ft

40°

22.

x6 ft60°


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Name _____________________________________________ Date _________________________

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23. 15 m

x

20°

24.

2 m

x

5°

25.

25°

11 yd

x

26.

63° 3 2 ydx

Use a cosine ratio to solve each problem. Round your answers to the nearest hundredth.

27. The path of a model rocket is shown below. How far east did the rocket travel?

28. An ichthyologist tags a shark and charts its path. Examine his chart below. How far south

did the shark travel?

21°

4230 ft

N

N

76°38 km

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29. A kite is flying 120 feet away from the base of its string, as shown below. How much string

is let out?

30. A pole has a rope tied to its top and to a stake 15 feet from the base. What is the length of

the rope?

15°120 ft

45°

15 ft


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Name _____________________________________________ Date _________________________

The Cosecant, Secant, and Cotangent RatiosAdditional Trigonometric Ratios

Vocabulary Define each term in your own words.

1. cosecant

2. secant

3. cotangent

Problem Set Write the cosecant ratio for each angle.

4. A

C B

csc B �

5. D

E F

csc D �

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6. G

H I

csc H �

7. J

L K

csc J �

Use the relationship between the cosecant and sine to write each trigonometric ratio.

8. csc A � 15 ___ 11

9. csc B � 12 ___ 5

sin A � sin B �

10. sin C � 6 ___ 19

11. sin D � 4 ___ 23

csc C � csc D �

Calculate the cosecant of each angle. If necessary, round your answer to the nearest ten thousandth.

12. The measure of �A is 24º and the measure of �B is 53º.

csc A �

csc B �

13. The measure of �C is 11º and the measure of �D is 62º.

csc C �

csc D �

14. The measure of �E is 58º and the measure of �F is 36º.

csc E �

csc F �


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Name _____________________________________________ Date _________________________

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15. The measure of �G is 72º and the measure of �H is 45º.

csc G �

csc H �

Write the secant ratio for each angle.

16. A

C B

sec A �

17. D

E F

sec F �

18. G

H I

sec H �

19. J

L K

sec J �

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Use the relationship between the secant and cosine to write each trigonometric ratio.

20. sec A � 14 ___ 3

cos A �

21. sec B � 9 __ 4

cos B �

22. cos C � 7 ___ 16

sec C �

23. cos D � 11 ___ 19

sec D �

Calculate the secant of each angle. If necessary, round your answer to the nearest ten thousandth.


sec A �

sec B �


sec C �

sec D �


sec E �

sec F �


sec G �

sec H �


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Name _____________________________________________ Date _________________________

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Write the cotangent ratio for each angle.

28. A

C B

cot B �

29. D

E F

cot D �

30. G

H I

cot H �

31. J

L K

cot J �

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Use the relationship between the cotangent and tangent to write each trigonometric ratio.

32. cot A � 3 __ 7

tan A �

33. cot B � 13 ___ 8

tan B �

34. tan C � 21 ___ 16

cot C �

35. tan D � 7 ___ 12

cot D �

Calculate the cotangent of each angle. If necessary, round your answer to the nearest ten thousandth.


cot A �

cot B �


cot C �

cot D �


cot E �

cot F �


cot G �

cot H �


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Name _____________________________________________ Date _________________________

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Complete each equation with the appropriate trigonometric function.

40. A

C B

sin A � B

41. D

E F

cos F � D

42. G

H I

cot G � H

43. J

L K

tan L � J

44. M

N O

sec O � M

45. P

Q R

csc P � R


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Name _____________________________________________ Date _________________________

Using a ClinometerAngles of Elevation and Depression

VocabularyA plane flies in a horizontal line. A cloud is above the plane and a lake is below the plane. Determine what the following measures.

1. angle of elevation

2. angle of depression

Problem SetUse the angle of elevation to solve each problem. Round your answers to the nearest hundredth.

3. You are standing 40 feet away from a building. The angle of elevation from the ground to

the top of the building is 57°. What is the height of the building?

4. A surveyor is 3 miles from a mountain. The angle of elevation from the ground to the top of

the mountain is 15°. What is the height of the mountain?

5. The angle of elevation from a ship to a 135-foot-tall lighthouse is 2°. How far is the ship

from the lighthouse?

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6. The Statue of Liberty is about 151 feet tall. If the angle of elevation from a tree in Liberty

State Park to the statue’s top is 1.5°, how far is the tree from the statue?

7. The angle of elevation from the top of a person’s shadow on the ground to the top of the

person is 45°. The top of the shadow is 50 inches away from the person. How tall is the

person?

8. A plane is spotted above a hill that is 12,000 feet away. The angle of elevation to the plane

is 28°. How high is the plane?

9. During the construction of a house, a 6-foot-long board is used to support a wall. The board

has an angle of elevation from the ground to the wall of 67°. How far is the base of the wall

from the board?

10. Museums use metal rods to position the bones of dinosaurs. If an angled rod needs to be

placed 1.3 meters away from a bone, with an angle of elevation from the ground of 51°,

what must the length of the rod be?

11. A 10-foot rope is used to tie down a shop sign. If the angle of elevation of the rope from the

ground is 75°, how high is the sign?


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Name _____________________________________________ Date _________________________

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12. A cable car connects a 425-foot-tall hill to a parking lot. If the angle of elevation from the

ground of the cable is 14°, what is the length of the cable?

Use the angle of depression to solve each problem. Round your answers to the nearest hundredth.

13. The angle of depression from the top of a building to a telephone line is 34°. If the building

is 25 feet tall, how far from the building does the telephone line reach the ground?

14. A airplane flying 3500 feet from the ground sees an airport at an angle of depression of 77°.

How far is the airplane from the airport?

15. To determine the depth of a well’s water a hydrologist measures the diameter of the well to

be 3 feet. She then uses a flashlight to point down to the water on the other side of the well.

The flashlight makes an angle of depression of 79°. What is the depth of the well water?

16. A zip wire from a tree to the ground has an angle of depression of 18°. If the zip wire ends

250 feet from the base of the tree, how far up the tree does the zip wire start?

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17. From a 50-foot-tall lookout tower, a park ranger sees a fire at an angle of depression of 1.6°.

How far is the fire from the tower?

18. The Empire State Building is 448 meters tall. The angle of depression from the top of the

Empire State Building to the base of the UN building is 74°. How far is the UN building from

the Empire State Building?

19. A factory conveyor has an angle of depression of 18° and drops 10 feet. How long is the

conveyor?

20. A bicycle race organizer needs to put up barriers along a hill. The hill is 300 feet tall and

from the top makes an angle of depression of 26°. How long does the barrier need to be?

fg10101...2 2 m 15 m d tan d 9. 5 5 ft 3 ft d tan d 10. 7 yd 15 yd f tan f 11. 2 6 yd 6 yd f tan f...

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