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Right Triangle Trigonometry PRACTICE TEST

Total questions: 55

Worksheet time: 1hrs 3mins

Name
Class
Date
1.

What is the ratio for Sine?

a)

Opposite Leg / Adjacent Leg

b)

Opposite Leg / Hypotenuse

c)

Adjacent Leg / Hypotenuse

d)

Adjacent Leg / Opposite Leg

e)

Hypotenuse / Adjacent Leg

2.

What is the ratio for Cosine?

a)

Opposite Leg / Adjacent Leg

b)

Opposite Leg / Hypotenuse

c)

Adjacent Leg / Hypotenuse

d)

Hypotenuse / Adjacent Leg

e)

Adjacent Leg / Opposite Leg

3.

What is the ratio for Tangent?

a)

Adjacent Leg / Opposite Leg

b)

Adjacent Leg / Hypotenuse

c)

Opposite Leg / Hypotenuse

d)

Opposite Leg / Adjacent Leg

e)

Hypotenuse/ Opposite Leg

4.

In right triangle DEF with right angle D. If

Tan D = 5/12, what is Tan F?

a)

12/5

b)

5/12

c)

12/13

d)

13/12

e)

5/13

5.

Solve for DE

a)

36.5

b)

18.8

c)

8.5

d)

7.9

e)

4.7

6.

Find m∠N

a)

18

b)

65

c)

76

d)

53

e)

72

7.

Find m∠S

a)

21

b)

69

c)

23

d)

67

e)

5/13

8.

A 16 foot ladder leans against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

e)

8.0

9.

A pilot looks down and sees the runway at an angle of depression of 10°. If the horizontal distance between the plane and the runway is 8000 feet, what is the height of the plane?

a)

1410.6

b)

1389.2

c)

5671.3

d)

7878.5

e)

888.8

10.

You decide to go to the city for a day of fun. You happen to be standing 30 feet away from a building that is 645 feet tall. What is your angle of elevation to the top of the building?

a)

87.3

b)

2.6

c)

79.1

d)

84.6

e)

5.4

11.

A traffic helicopter spots two different accidents. One is east at an angle of depression of 35 degrees. The other is west at an angle of depression of 21 degrees. If the helicopter is 800 feet in the air, how far apart are the accidents?

a)

1142

b)

2084

c)

3226

d)

942

e)

4168

12.

Determine the value of: sin(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

13.

Determine the value of: cos(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

14.

Determine the value of: tan(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

15.

Consider angle B in the diagram below.

What is the length of "opposite side" to angle B?

a)

6

b)

8

c)

10

d)

not possible to determine

e)

Sine

16.

Consider angle B in the diagram below.

What is the length of "adjacent side" to angle <B?

a)

6

b)

8

c)

10

d)

not possible to determine

e)

pythagorean theorem

17.

Which trigonometric function would you use to find "h", the height of the tree?

a)

sine

b)

cosine

c)

tangent

d)

none of these

e)

pythagorean theorem

18.

Which inverse trig function would you use to find the measure of Angle A?

a)

inverse sine

b)

inverse cosine

c)

inverse tangent

d)

It is not possible to determine m<A

e)

pythagorean theorem

19.

Which is the best strategy to use for finding the length of the missing side?

a)

sine

b)

cosine

c)

tangent

d)

pythagorean theorem

e)

not enough information

20.

Which trig ratio or function should you use to find the value of "h"?

a)

sine

b)

cosine

c)

tangent

d)

an inverse trig function

e)

pythagorean theorem

21.

What is the most efficient way to find "x"?

a)

Inverse sine

b)

sine

c)

Inverse tangent

d)

pythagorean theorem

e)

tangent

22.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

e)

6.66 m

23.

Choose the correct ratio in calculator ready form:

a)

14 sin (37)

b)

14 cos (37)

c)

14 / (tan 37)

d)

14 / (sin 37)

e)

14 / (cos 37)

24.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

e)

23.5 cm

25.

Solve for the misssing distance

a)

18.9

b)

19.5

c)

47

d)

27.5

e)

23.3

26.

What is the correct equation to solve for x ?

a)

tan( 46 ) = 17/x

b)

sin ( 46 ) = x/17

c)

tan (46 ) = x/17

d)

cos (46) = x/17

e)

172+172=x2

27.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Pythagorean Theorem

e)

Inverse Tangent

28.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

180 - 90- 50 = r

e)

Pythagorean Theorem

29.

What type of triangle is the context of our study of trigonometry?

a)

right triangle

b)

isosceles triangle

c)

scalene triangle

d)

acute triangle

e)

obtuse triangle

30.

If you are given the length of a hypotenuse and the length of an adjacent side, what trigonometry ratio could you use to find an angle?

a)

sine

b)

cosine

c)

tangent

d)

SAHCOHTOA

e)

pythagorean theorem

31.

Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.

a)

19 degrees

b)

20 degrees

c)

28 degrees

d)

35 degrees

e)

70 degrees

32.

Spencer is going snowboarding. He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet. The angle of elevation from the bottom to the top of the mountain is 25o. What is the length of the Spencer’s run (his trip down the hill)?

a)

3216.76 feet

b)

633.93 feet

c)

699.46 feet

d)

3549.30 feet

e)

1655.07 feet

33.

A golfer is standing at the tee, looking up to the green on a hill. If the tee is 36 yards lower than the green and the angle of elevation from the tee to the hole is 12°, find the distance from the tee to the hole in feet.

a)

173.15 feet

b)

7.48 feet

c)

22.95 feet

d)

508.11 feet

e)

519.45 feet

34.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

a)

60 feet

b)

45 feet

c)

100 feet

d)

135 feet

e)

44 feet

35.

A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower

a)

18.01 m

b)

29.89 m

c)

13.38 m

d)

22.21 m

e)

26.91 m

36.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

e)

93 ft

37.

The pilot of a traffic helicopter sights an accident at an angle of depression of 18 degrees. The helicopter’s altitude is 1560 ft. What is the horizontal distance from the helicopter to the accident? Round to the nearest foot.

a)

543 ft

b)

1756 ft

c)

4801 ft

d)

5404 ft

e)

5048 ft

38.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

20 degrees

e)

70 degrees

39.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

e)

13 ft

40.

An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building?

a)

5.71

b)

16.70

c)

17.46

d)

21.84

e)

5.74

41.

Which trigonometric ratio are correct for the triangle? (select all that apply)

a)

sin A = c/b

b)

sin A = a/c

c)

tan A = a/b

d)

cos B = a/c

e)

cos A = a/c

42.

the angle formed by a horizontal line and a line of sight to a point above

a)

Angle of Depression

b)

Angle of Elevation

c)

Adjacent Angles

d)

Vertical Angles

e)

Supplementary Angles

43.

the angle formed by a horizontal line and a line of sight to a point below

a)

Complementary Angle

b)

Adjacent Angle

c)

Angle of Depression

d)

Angle of Elevation

e)

Supplementary Angle

44.

Students are trying to determine the height of the flagpole at Arlington High. They have measured out a horizontal distance of 40 feet from the flagpole and site the top of it at an angle of elevation of 52 degrees. Which below is closest to the height, h, of the flagpole?

a)

31.5 feet

b)

24.6 feet

c)

51.2 feet

d)

57.4 feet

e)

65.0 feet

45.

Check all answers that are true

a)

∠R= Angle of Depression

b)

∠S= Angle of Elevation

c)

∠T= Angle of Depression

d)

∠W= Angle of Elevation

e)

∠T= Angle of Elevation

46.

Name the angle of depression

a)

∠F

b)

∠L

c)

∠S

d)

∠T

e)

not enough information

47.

Which of the following statements are true?

a)

∠A is an angle of elevation

b)

∠B is an angle of elevation

c)

∠C is the angle of depression

d)

∠D is the angle of depression

e)

∠C is the angle of elevation

48.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
e)

x= 59

49.

Set up an equation that could be used to solve for the variable. Choose all answers that are true

a)
b)
c)
d)
e)

x = 12.88

50.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
e)

None of the above, cosine must be used to solve this triangle.

51.

Set up an equation that could be used to solve for the variable, place your answer in calculator ready form

a)

x= 10.3 Sin (37)

b)

x= 10.3 / (Sin (37))

c)

x= 10.3 / Cos (37)

d)

x= 37 / (Cos (10.3))

e)

x= 37 Tan (10.3)

52.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
e)

Tangent is not the correct trigometric ratio for the given triangle!

53.

Your family wants to purchase a new laptop with a 17” widescreen. Since the 17 inches represents the diagonal measurement of the screen. You want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don’t remember the width. What is the width of your new laptop?

a)

13.7 inches

b)

12.8 inches

c)

11.3 inches

d)

13.1 inches

e)

17.0 inches

54.

Solve the right triangle

a)

c=21.7, b=14, ∠B=-55

b)

c=12.2, b=10, ∠B=35

c)

c=12.2, b=10, ∠B=55

d)

c=10, b=12.2, ∠B=35

e)

c=12.2, b=10, ∠B=55

55.

In right triangle DEF with right angle D. If

Tan D = 5/12, what is Cos F=?

a)

12/5

b)

5/12

c)

12/13

d)

13/12

e)

5/13

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