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Solving Right Triangle Problems Quiz

Total questions: 100

Worksheet time: 2hrs 11mins

Name
Class
Date
1.

If you are given the hypotenuse and an adjacent side, which trigonometric function should you use to find the angle?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

e)

Pythagorean theorem

2.

Find Cos(A) as a decimal rounded the the nearest ten-thousandth.

a)

.4706

b)

1.875

c)

.8824

d)

.5333

e)

61.92

3.
a)

A

b)

B

c)

C

d)

D

e)

none of the above

4.

Choose all of the correct ratios for the triangle in the picture

a)

Sin (B) =21/29

b)

Sin (B) =20/29

c)

Cos (A) =21/29

d)

Tan (B) =21/29

e)

Tan (A) =21/20

5.

If you are given the hypotenuse and an adjacent side, which should you use to find the the other side length?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

e)

Pythagorean theorem

6.

Which is the calculator ready form to solve this problem for x?

a)

22 Tan (12)

b)

12 tan (22)

c)

tan(12) / 22

d)

22/ tan (12)

e)

none of the above

7.

cos 40⁰ = ?

a)

sin 50⁰

b)

cos 50⁰

c)

tan 50⁰

d)

sin 40⁰

e)

tan 40⁰

8.

Find the measure of the missing angle.

a)

49o

b)

50o

c)

41o

d)

33o

e)

57o

9.

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)

45 degrees

d)

70 degrees

e)

71 degrees

10.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

e)

34.1

11.

Solve for the missing distance for the depth of the anchor.

a)

18.9 m

b)

19.5 m

c)

47 m

d)

27.5 m

e)

24.3 m

12.

Which of the following is the calculator ready form to solve the height of the airplane?

a)

1000Sin(60)

b)

1000/Sin(60)

c)

1000Cos(60)

d)

1000/Cos(60)

e)

1000/Tan(60)

13.

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)

125 ft

14.

Henry knows the angle of depression from the lookout and also knows from that angle it is 45 feet in the air. About how far is he from the middle of the lookout tower?

a)

30 feet

b)

45 feet

c)

38 feet

d)

54 feet

e)

59 feet

15.

A princess is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at her, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?

a)

30 feet

b)

17.3 feet

c)

8.7 feet

d)

7.5 feet

e)

26.0 feet

16.

Jose would like to know the height of the brick building shown in the picture, if the angle of elevation is 50 degrees and he is 36 feet from the building. Which of these is the calculator ready expression to find the building height?

a)

36 Sin (50)

b)

36 Tan (50)

c)

36 Sin (50) + 6

d)

36 Tan (50) + 6

e)

36 Cos (50) + 6

17.

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

18.

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

19.

Solve for DE

a)

36.5

b)

18.8

c)

8.5

d)

7.9

e)

4.7

20.

Find m∠S

a)

21

b)

69

c)

23

d)

67

e)

5/13

21.

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

22.

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

23.

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

24.

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

25.

Determine the value of: sin(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

26.

Determine the value of: cos(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

27.

Determine the value of: tan(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

e)

7 / 24

28.

Consider angle B in the diagram below.

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

a)

6

b)

8

c)

10

d)

CB

e)

Sine

29.

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

30.

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

31.

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

32.

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

33.

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

34.

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

a)

Inverse sine

b)

sine

c)

Inverse tangent

d)

pythagorean theorem

e)

tangent

35.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

e)

6.66 m

36.

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)

37.

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

38.

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

39.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Pythagorean Theorem

e)

Inverse Tangent

40.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

180 - 90- 50 = r

e)

Pythagorean Theorem

41.

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

42.

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

43.

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

44.

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

45.

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

46.

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

47.

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

48.

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

49.

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

50.

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

51.

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

52.

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

53.

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

54.

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

55.

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

56.

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

57.

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

58.

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

a)
b)
c)
d)
e)

x= 59

59.

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

60.

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.

61.

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)

62.

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!

63.

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

64.

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

65.

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

66.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

e)

tan(37)=14/x

67.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

e)

16

68.

A rectangular field is 50 yards wide and 100 yards long. Ethan walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

e)

150 yards

69.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Cah Toh

e)

Sah Coa Toh

70.

From ∠C, what side is AB?

a)

Adjacent

b)

Hypotenuse

c)

Opposite

d)

Vertical

e)

Supplementary

71.

Give the Ratio for SIN X

a)

opp/adj

b)

adj/hyp

c)

opp/hyp

d)

adj/opp

e)

hyp/adj

72.

Give the Ratio for TAN X

a)

Adj/Opp

b)

Opp/Adj

c)

Adj/Hyp

d)

Opp/Hyp

e)

Hyp/Opp

73.

Give the Ratio for COS X

a)

Adj/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Opp/Hyp

e)

Hyp/Adj

74.

Based on the diagram, choose all the statements that are true.

a)
b)
c)
d)
e)
75.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

e)

tan X = 28/41

76.

Right triangle ABC is shown below. Which equation gives the correct value for BC?

a)
b)
c)
d)
e)

Not enough information to solve BC

77.

Find Tan A

a)

21/20

b)

29/20

c)

21/29

d)

20/21

e)

20/29

78.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

e)

Multiply that leg by √3

79.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

e)

Multiply that leg's length by √3.

80.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 3√2 y = 3

c)

x = 3√3 y = 6

d)

x = 6 y = 3√2

e)

x = 6√3 y = 6

81.

What are a and b in this 30-60-90 triangle?

a)

b=3.5√3 a = 7√3

b)

b = 7 a = 7√2

c)

b = 7 a = 14

d)

b = 7√3 a = 14√3

e)

b = 7 a = 14√6

82.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

e)

12

83.

How long is e?

a)

3

b)

6

c)

6√3

d)

6√2

e)

9

84.

What is the measure of side c?

a)

7

b)

72\frac{7}{\sqrt{2}}

c)

727\sqrt{2}

d)

14

e)

73\frac{7}{\sqrt{3}}

85.

What is the measure of a?

a)

3

b)

333\sqrt{3}

c)

6

d)

323\sqrt{2}

e)

232\sqrt{3}

86.

How long is side c?

a)

1

b)

2

c)

2\sqrt{2}

d)

3\sqrt{3}

e)

3

87.

Find n.

a)

4

b)

6

c)

12

d)

232\sqrt{3}

e)

7

88.

Find the length of m.

a)

4

b)

6

c)

12

d)

232\sqrt{3}

e)

24

89.

Which equation can be used to solve the word problem: the diagonal of a t.v. is 40 inches and the height is 30. How wide is the t.v.? Choose all that could be used!

a)

302 + 402 = c2

b)

a2 + 402 = 302

c)

302 + b2 = 402

d)

402 + 302 = c2

e)

a2 + 302 = 402

90.

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

a)

6

b)

6.7

c)

3

d)

15.7

e)

None of them

91.

Acute, right, or obtuse

a)

Acute Triangle

b)

Right Triangle

c)

Obtuse Triangle

d)

Not a Triangle

e)

Isosceles Triangle

92.

If the legs of a right triangle are 10 and 24, then the hypotenuse is __________.

a)

21

b)

19

c)

26

d)

30

e)

34\sqrt{34}

93.

Which set of side lengths form a right triangle? Choose ALL that apply!

a)

4, 8, 12

b)

12, 13, 20

c)

20, 21, 29

d)

48, 55, 74

e)

3, 4, 5

94.

What type of triangle do these measurements make: 6, 9, 17

a)

acute triangle

b)

right triangle

c)

obtuse triangle

d)

not a triangle

e)

isosceles triangle

95.

Determine if the lengths shown create an acute, obtuse, or right triangle.

a)

Acute Triangle

b)

Obtuse Triangle

c)

Right Triangle

d)

Not a Triangle

e)

Isosceles Triangle

96.

Solve for x. Round to the nearest tenth.

a)

x = 44.6

b)

x = 29.4

c)

x = 36.2

d)

x = 22.3

e)

x = 38.4

97.

A bee is in a box shaped as a rectangular prism. The box measures 30 inches by 14 inches by 40 inches. The bee flies from one corner of the box to the corner that is the farthest away. To the nearest inch, how far does the bee fly (r)?

a)

17 in.

b)

45 in.

c)

38 in.

d)

52 in.

e)

84\sqrt{84}

98.

A bee is in a box shaped as a rectangular prism. The box measures 30 inches by 14 inches by 40 inches. The bee flies from one corner of the box to the other corner on the bottom. What is the the length of the bee's flight (s) to the closest inch?

a)

17 in.

b)

45 in.

c)

38 in.

d)

52 in.

e)

42 in.

99.

What are the three angle measures of the triangle formed using the sides h, s, r

a)

90

b)

53

c)

35

d)

37

e)

55

100.

A rectangular field is 50 yards wide and 100 yards long. Ethan walks diagonally across the field. Given the diagonal forms a triangle with the length and width, what is the smallest angle in the triangle?

a)

90 Degrees

b)

30 Degrees

c)

45 Degrees

d)

27 Degrees

e)

33 Degrees

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