Math 2B/3A

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

Trigonometry Quiz Review Packet

Basic skills: * Find missing side lengths and angle measures of 45-45-90 and 30-60-90 triangles. * Find missing side lengths of figures using trigonometric ratios. * Find missing angle measures of figures using inverse trigonometry ratios. * Find the area of triangles using trigonometry. * Model and solve real world problems using trigonometry. Practice Problems: YOU MUST complete this on a SEPARATE SHEET OF PAPER! 1. Find the missing side lengths. Give exact, simplified answers.

a. a.

b. b.

c. c.

d. d.

e. e.

f. f.

2. Find all the missing side lengths in the diagram below. Give exact, simplified answers.

x

y

x

y w

z

v

t

r

q

Math 2B/3A

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

3. Use trigonometry to solve for the missing value. Round to two decimal places. Be careful; in some of

these you’re just using trig ratios but in others you need to use inverse trig!

a.

b.

c.

d.

e.

f.

g.

h.

i.

4. a. Write two different trig equations that would allow you to solve for b. Hint: Find the missing angle first. b. Write two different trig equations that would allow you to solve for c. 5. Find each of the following in terms of a, b, and c. sinα = cosα = tanα = sinβ = cosβ = tanβ =

6. ΔJKL is a right triangle with its right angle at K, and sin(L) = 35

.

a. Sketch a possibleΔJKL and label all the information you know. b. Find and label all the side lengths. c. Find each of the following values: cos(L) , tan(J ) , and sin(J ) . d. Use inverse trig to find the measures of angles L and J.

Math 2B/3A

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

32º40º

a

b 44

C B

A

7. Solve for a and b in the triangle below. Hint: Split each triangle into two right triangles first so you can use trig!

8. Find the area of ΔLMN rounded to two decimal places. 9. Find the area of ΔLMN rounded to two decimal places. 10. A triangle has sides of length 12 inches and 10 inches. The angle between these side lengths

measures 38 degrees. Find the area of the triangle, rounded to two decimal places. 11. A ramp to a loading dock must slant at a 10° angle.

a. If the ramp meets the ground 25 feet from the base of the building, how long is the ramp? b. Construction workers are building a different ramp up to a door that is 2 feet off the

ground. Find the length of the ramp. 12. A ladder is leaning against a house so that the distance from the base of the ladder to the house

is 7 feet. The ladder is 15 feet tall. a. Find the angle the ladder makes with the ground. b. How high up the side of the house does the ladder reach?

Math 2B/3A

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

Trigonometry Quiz Review Answers

1.

a. 𝑥 = 3,𝑦 = ! !!

b. 𝑥 = 𝑦 = 2 3 c. 𝑢 = 16, 𝑣 = 8 3 d. 𝑥 = !" !"

!,𝑦 =   ! !"

!

e. 𝑥 = ! !!

f. 𝑥 = 3 3,𝑦 = 6 3

2. 𝑥 = 2 2,𝑦 = 4 2, 𝑧 = 4 2,𝑤 = 8,   𝑣 = 4 3, 𝑡 = 4, 𝑞 = 𝑟 = 2 2

3. a. ℎ = 9.23  b. 𝑦 = 76.34  c. 𝑢 = 37.87° d. 𝑥 = 27.92 e. 𝑤 = 18.00 f. 𝑦 = 33.69° g. 𝑧 = 22.84 h. ℎ = 3.51 i. 𝑣 = 47.38

4.

a. tan 59° = !!, tan 31° = !

!

b. sin(31°) = !!, cos 59° = !

!

5. sin 𝛼 = !

!

cos 𝛼 = !!

tan 𝛼 = !!

sin 𝛽 = !!

cos 𝛽 = !!

tan 𝛽 = !!

6. a. & b.

c. cos 𝐿 = !

!, tan 𝐽 = !

!, sin 𝐽 = !

!

d. 𝐿 = 36.87°, 𝐽 = 53.13° 7. 𝑎 = 65.10, 𝑏 = 36.28 8. Area = 18.91 units2 9. Area = 8.64 cm2 10. Area = 36.94 in2 11.

a. 25.39 ft b. 11.52 ft

12. a. 62.18° b. 13.27 ft