Trigonometry Quiz

Question 1

In a right-angled triangle, what does SOH-CAH-TOA stand for?

Accepted Answer

Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent

Answer

Side Over Hypotenuse — Cosine Adjacent Hypotenuse — Tangent Opposite Adjacent

Answer

Sine = Adjacent/Opposite, Cosine = Hypotenuse/Adjacent, Tangent = Adjacent/Hypotenuse

Answer

Sum Of Hypotenuse — Cosine And Hypotenuse — Tangent Of Angles

Question 2

A right-angled triangle has an angle of 30° and a hypotenuse of 10 cm. What is the side opposite the 30° angle?

Accepted Answer

5 cm

Answer

5√3 cm

Answer

√3 cm

Answer

8.66 cm

Question 3

What is the exact value of sin(30°)?

Accepted Answer

1/2

Answer

√3/2

Answer

1/√2

Answer

√3

Question 4

What is the exact value of cos(60°)?

Accepted Answer

1/2

Answer

√3/2

Answer

1/√2

Answer

0

Question 5

A right-angled triangle has adjacent side 8 cm and hypotenuse 10 cm. What angle is at the top?

Accepted Answer

37°

Answer

30°

Answer

53°

Answer

60°

Question 6

What is tan(45°)?

Accepted Answer

1

Answer

0

Answer

1/2

Answer

√3

Question 7

A ladder 5 m long leans against a wall. The base is 3 m from the wall. What angle does the ladder make with the ground?

Accepted Answer

53°

Answer

30°

Answer

37°

Answer

60°

Question 8

What is the sine rule?

Accepted Answer

a/sin A = b/sin B = c/sin C

Answer

a² = b² + c² − 2bc cos A

Answer

sin A/a = sin B/b

Answer

Both A and C are correct

Question 9

What is the cosine rule?

Accepted Answer

a² = b² + c² − 2bc cos A

Answer

a = b + c − 2bc cos A

Answer

cos A = (b + c − a) / 2bc

Answer

a² = b² + c²

Question 10

A right-angled triangle has opposite = 7 cm and adjacent = 24 cm. What is the angle opposite the 7 cm side?

Accepted Answer

16.3°

Answer

17.1°

Answer

72.9°

Answer

73.7°

Question 11

What is the exact value of tan(60°)?

Accepted Answer

√3

Answer

1/√3

Answer

1

Answer

2

Question 12

A triangle has sides a = 7, b = 8, c = 5. Which formula would you use to find angle A?

Accepted Answer

Cosine rule: cos A = (b² + c² − a²) / 2bc

Answer

SOH-CAH-TOA

Answer

Sine rule only

Answer

Pythagoras' theorem

Question 13

A right-angled triangle has hypotenuse 13 cm and one side 5 cm. What is the other side?

Accepted Answer

12 cm

Answer

8 cm

Answer

√194 cm

Answer

√144 cm

Question 14

What is the area formula for a triangle using trigonometry?

Accepted Answer

½ab sin C

Answer

½ × base × height

Answer

½ab cos C

Answer

ab sin C

Question 15

A triangle has sides 6 cm and 8 cm with an included angle of 30°. What is its area?

Accepted Answer

12 cm²

Answer

24 cm²

Answer

48 cm²

Answer

6 cm²

Question 16

What is the exact value of cos(45°)?

Accepted Answer

1/√2

Answer

1/2

Answer

√3/2

Answer

√2

Question 17

From the top of a 50 m cliff, a boat is observed at an angle of depression of 30°. How far is the boat from the base of the cliff?

Accepted Answer

50√3 m

Answer

25 m

Answer

25√3 m

Answer

100 m

Question 18

In which quadrant is sin(θ) negative and cos(θ) positive?

Accepted Answer

Quadrant IV

Answer

Quadrant I

Answer

Quadrant II

Answer

Quadrant III

Question 19

What is sin²(θ) + cos²(θ) equal to?

Accepted Answer

1

Answer

0

Answer

2

Answer

tan(θ)

Question 20

A surveyor stands 100 m from a building and measures the angle of elevation to the top as 40°. How tall is the building? (tan 40° ≈ 0.84)

Accepted Answer

84 m

Answer

119 m

Answer

65 m

Answer

77 m