Free Printable Unit 8 Review - Trigonometry & Right Triangles

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

2.

What is the ratio for Cosine?

a)

Opposite Leg / Adjacent Leg

b)

Opposite Leg / Hypotenuse

c)

Adjacent Leg / Hypotenuse

d)

Hypotenuse / Adjacent 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

4.

In Right Triangle ABC with right angle C. If the

Cos A = 9/41, what is the Sin B?

a)

40/41

b)

41/9

c)

9/41

d)

40/9

5.

In right triangle DEF with right angle D. If
Tan E = 5/12, what is Tan F?

a)

12/5

b)

5/12

c)

12/13

d)

13/12

6.

Solve for DE

a)

36.5

b)

18.8

c)

8.5

d)

7.9

7.

Solve for WI

a)

7.9

b)

12.7

c)

6.2

d)

16.2

8.

Find m∠N

a)

14

b)

65

c)

76

d)

53

9.

Find m∠S

a)

21

b)

69

c)

23

d)

67

10.

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

11.

A pilot looks down and sees the runway approaching. The angle between the plane's diagonal and vertical line of sight is 80°. 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

12.

A traffic helicopter spots two different accidents. One is east at an angle of elevation of 55 degrees. The other is west at an angle of elevation of 69 degrees. If the helicopter is 800 feet in the air, how far apart are the accidents?

a)

1142

b)

2084

c)

3226

d)

942

13.

a)

A

b)

B

c)

C

d)

D

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

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

a)

.4706

b)

1.875

c)

.8824

d)

.5333

17.

What is the cosine of θ?

a)

15/8

b)

15/17

c)

17/15

d)

8/15

18.

What is the tangent of angle C?

a)

7/25

b)

25/7

c)

7/24

d)

24/7

19.

What is the sine of A?

a)

7√65∕65

b)

7/65

c)

√7/65

d)

√65/7

20.

If tanθ = 3/4, what is cosθ?

a)

3/5

b)

4/5

c)

4/3

d)

not enough information

21.

What is the value of "y" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

22.

What is the value of "x" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

23.

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

a)

sine

b)

cosine

c)

tangent

d)

none of these

24.

How would you find "x" in the diagram?

a)

Multiply 15 by 2.

b)

Divide 15 by 2.

c)

Multiply 15 by √3.

d)

Divide 15 by √3.

25.

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

26.

True or False. To find the missing side length in the diagram, use the Pythagorean Theorem.

a)

True

b)

False

27.

Which expression is correct for "y"?

a)

y = tan^–1(31/23)

b)

y = sin^–1(31/23)

c)

y = cos^–1(31/23)

28.

How would you find the value of the angle denoted by "?"

a)

Apply the inverse sine

b)

Apply the inverse cosine

c)

Apply the inverse tangent

d)

Apply the Pythagorean Theorem

29.

How would you find "x" in this Special Right Triangle?

a)

Divide 10 by 2.

b)

Multiply 10 by 2.

c)

Multiply 10 by √3

d)

Divide 10 by √3

30.

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

a)

Inverse sine

b)

Inverse cosine

c)

Inverse tangent

d)

Pythagorean Theorem

31.

You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 175 feet tall. You measure the angle of elevation to the top of the lighthouse at 5^o. How far are you from the bottom of the lighthouse?

a)

2000.3 feet

b)

2007.3 feet

c)

1997.9 feet

d)

2134.8 feet

32.

You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 3^o. How tall is the enemy castle wall?

a)

78.6 meters

b)

1498.0 meters

c)

78.5 meters

d)

75.3 meters

33.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

34.

We can use SOH-CAH-TOA for...

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

35.

A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

a)

134.4

b)

67.2

c)

95√2

d)

(95√2)/2

36.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

37.

Find the value of y.

a)

7

b)

7√3

c)

14√3

d)

(14√3)/3

38.

Find the value of y.

a)

11√2

b)

11

c)

22

d)

(11√2)/2

39.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

40.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

41.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

42.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

43.

Find x.

a)

10

b)

√3

c)

5

d)

10√3

44.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

45.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

46.

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

47.

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

48.

A triangle has the following side lengths:
AB = 12 units
BC = 10 units
AC = 16 units
What type of triangle does this make?

a)

Acute

b)

Obtuse

c)

Right

49.

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

a)

8√2

b)

4√2

c)

4

d)

8

50.

A triangle has side lengths:
5, 8, 6. Is this triangle a right triangle, an acute triangle, or an obtuse triangle?

a)

right

b)

acute

c)

obtuse

51.

A triangle has side lengths:
20, 21, 28. Is this triangle a right triangle, an acute triangle, or an obtuse triangle?

a)

right

b)

acute

c)

obtuse

52.

1

a)

A

b)

B

c)

C

d)

D

53.

2

a)

A

b)

B

c)

C

d)

D

54.

3

a)

A

b)

B

c)

C

d)

D

55.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

56.

Find AC

a)

12

b)

10

c)

23

d)

14

57.

Find AB

a)

10

b)

8

c)

6.1

d)

4.9

58.

LoS: Find AB.

a)

11.3

b)

12.3

c)

13.3

d)

14.3

59.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

60.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

61.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

62.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

63.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49^o and Stake B measures an angle of elevation of 58^o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

a)

152.7 feet

b)

166.3 feet

c)

157.3 feet

d)

131.7 feet

64.

Find BC

a)

A

b)

B

c)

C

d)

D

65.

Find angle A

a)

53.6

b)

13.3

c)

113.1

66.

What are the possible criteria for the Law of Cosines?

a)

SSA, SSS

b)

SSA, ASA

c)

SSS, SAS

d)

AAS, ASA

67.

What are the possible criteria for Law of Sines?

a)

SSA, ASA, AAS

b)

AAS, SSS, ASA

c)

SAS, SSS, ASA

d)

SAS, AAS, ASA

68.

To approximate the length of a marsh, a surveyor walks 425 meters from point A to point B. Then the surveyor turns 65º and walks 300 meters to point C. Approximate the length AC of the marsh.

a)

250

b)

615

c)

:)

d)

Not me

69.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

70.

Use Law of Cosines to find angle T

a)

62.2°

b)

53.1°

c)

59.5°

d)

64.7°

71.

Find the missing side.

a)

15.9 in.

b)

22.8 in.

c)

19.2 in.

d)

521.1 in.

72.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

a)

9285.73 ft

b)

96.36 ft

c)

24061.81 ft

d)

155.12 ft

73.

Solve for "B" if:

a = 4, b = 5, and c = 8.

a)

47.5^o

b)

125.1^o

c)

30.8^o

d)

24.1^o

74.

Solve for "C" if:

a = 9.4, b = 10, and c = 4.

a)

86.7^o

b)

23.5^o

c)

5.8^o

d)

.99^o

Unit 8 Review - Trigonometry & Right Triangles

Total questions: 74

Worksheet time: 6hrs 38mins

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