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Secondary Math 2

Unit 11 - Trigonometry Review

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-1-

Use the Pythagorean Theorem to find the length of the missing side of each triangle. Leave your

answers in simplest radical form (simplified roots).

1)

1630

x

2)

6

x

2 3

Find the distance between each pair of points. Round your answers to the nearest tenth, if necessary.

3) (−8, 2) and (7, −6) 4) (0, −3) and (−2, −5)

Find the missing side lengths using special right triangle patterns. Leave your answers as radicals in

simplest form (simplified roots).

5)

8 2

x

y

45°

6)

m10

n

45°

7)

9

x y

45°

8)

m3 2

n

45°

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9)

m

n

260°

10)

10

m

n60°

11)

x

y 5 6

60°

12)

x

15y

60°

Find the value of the requested trigonometric function. Write exact answers (simplified fractions

with simplified roots).

13) tan θ20

1612

θ

14) cos θ

3

2

θ

15) sin θ

14

6 5

θ

Find the measure of each angle indicated to the nearest tenth of a degree.

16)

125

A

B

Cθ

17)

14

8

B A

C

θ

18)

2.6

7.4A

B

C

θ

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Write an equation involving sine, cosine, or tangent that can be used to find the missing side length.

Then solve the equation. Round your answers to the nearest tenth.

19)

19 x

48°

20)

x13

40°

21)

18x

33°

22)

18x

34°

23)

x11

25°

24)

x

15

66°

1) Draw and label a triangle to illustrate the situation. 2) Find the length of the missing side. 3) Give

the values of the requested functions. 4) Give the measure of the angle to the nearest tenth of a

degree.

25) tan θ = 24

7. Find sin θ , cos θ , and the measure of θ .

26) sin θ = 28

53. Find cos θ , tan θ , and the measure of θ .

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Solve the triangle. (Make sure to label all missing pieces and show all work). Round your answers to

the nearest tenth.

27)

7

A B

C

21°

28)

12.4

6.7

B

A

C

Draw a diagram to help you solve each problem. Then write an equation and give your answer to the

nearest tenth. Don't forget to include the correct units.

29) A 20-ft. tall ladder is leaning against a building. It makes a 65° angle with the ground. How far up the

building does it reach?

30) A baseball diamond is a square with sides of length 90 ft. The catcher attempts to catch a runner

stealing by throwing from home plate to second base. How long is the throw?

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31) A photographer wishes to take a picture of a bird in a tree. She is standing 15 feet away from the tree

and the angle of elevation from the camera to the bird is 50°. How far is the camera from the bird?

32) The chairlift at a ski resort has a vertical rise of 3900 ft. If the length of the ride is 6350 ft., what is the

angle of elevation of the lift?