Trigonometry Quiz

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

1. Side Over Hypotenuse — Cosine Adjacent Hypotenuse — Tangent Opposite Adjacent
2. Sine = Adjacent/Opposite, Cosine = Hypotenuse/Adjacent, Tangent = Adjacent/Hypotenuse
3. Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent
4. Sum Of Hypotenuse — Cosine And Hypotenuse — Tangent Of Angles

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

1. √3 cm
2. 5 cm
3. 5√3 cm
4. 8.66 cm

3. What is the exact value of sin(30°)?

1. √3
2. √3/2
3. 1/√2
4. 1/2

4. What is the exact value of cos(60°)?

1. √3/2
2. 0
3. 1/√2
4. 1/2

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

1. 30°
2. 37°
3. 53°
4. 60°

6. What is tan(45°)?

1. √3
2. 0
3. 1
4. 1/2

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?

1. 30°
2. 37°
3. 53°
4. 60°

8. What is the sine rule?

1. a/sin A = b/sin B = c/sin C
2. a² = b² + c² − 2bc cos A
3. Both A and C are correct
4. sin A/a = sin B/b

9. What is the cosine rule?

1. a = b + c − 2bc cos A
2. a² = b² + c²
3. a² = b² + c² − 2bc cos A
4. cos A = (b + c − a) / 2bc

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

1. 16.3°
2. 17.1°
3. 72.9°
4. 73.7°

11. What is the exact value of tan(60°)?

1. √3
2. 1
3. 1/√3
4. 2

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

1. Cosine rule: cos A = (b² + c² − a²) / 2bc
2. Pythagoras' theorem
3. Sine rule only
4. SOH-CAH-TOA

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

1. √144 cm
2. √194 cm
3. 12 cm
4. 8 cm

14. What is the area formula for a triangle using trigonometry?

1. ½ × base × height
2. ½ab cos C
3. ½ab sin C
4. ab sin C

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

1. 12 cm²
2. 24 cm²
3. 48 cm²
4. 6 cm²

16. What is the exact value of cos(45°)?

1. √2
2. √3/2
3. 1/√2
4. 1/2

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?

1. 100 m
2. 25 m
3. 25√3 m
4. 50√3 m

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

1. Quadrant I
2. Quadrant II
3. Quadrant III
4. Quadrant IV

19. What is sin²(θ) + cos²(θ) equal to?

1. 0
2. 1
3. 2
4. tan(θ)

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)

1. 119 m
2. 65 m
3. 77 m
4. 84 m