SSC CGL - Trigonometric Ratios, Heights and Distances Online Test (MCQ Quiz)

1. In a right-angled triangle, if the angle theta is such that sin(theta) = 3/5, what is the value of cos(theta)?

A) 3/5 B) 4/5 C) 5/4 D) 5/3

2. If tan(theta) = 1, what is the value of theta in degrees?

A) 30° B) 45° C) 60° D) 90°

3. What is the value of sin²(theta) + cos²(theta)?

A) 0 B) 1 C) sin(theta) D) cos(theta)

4. If sec(theta) = 13/12, what is the value of tan(theta) in a right-angled triangle where theta is acute?

A) 5/12 B) 12/5 C) 13/5 D) 5/13

5. The angle of elevation of the sun is 60°. If a vertical pole casts a shadow of length 10 meters, what is the height of the pole?

A) 10√3 meters B) 10/√3 meters C) 20/√3 meters D) 20√3 meters

6. If cos(theta) = 8/17, what is the value of sin(theta) for an acute angle theta?

A) 8/17 B) 15/17 C) 17/8 D) 17/15

7. What is the value of tan(60°) + cot(30°)?

A) 2√3 B) √3 C) 2 D) 3

8. If sin(theta) = 1/2, what is the value of theta in degrees?

A) 30° B) 45° C) 60° D) 90°

9. In a right-angled triangle ABC, right-angled at B, if AB = 5 and BC = 12, what is the value of tan(C)?

A) 5/12 B) 12/5 C) 5/13 D) 12/13

10. If the angle of elevation of a tower from a point 100 meters away from its base is 45°, what is the height of the tower?

A) 50 meters B) 100 meters C) 100√2 meters D) 200 meters

11. What is the value of sin(30°) * cos(60°)?

A) 1/4 B) 1/2 C) 3/4 D) 1

12. If tan(theta) = √3, what is the value of cot(theta)?

A) √3 B) 1/√3 C) 1 D) 0

13. The angle of depression of an object on the ground from a point 50 meters high is 30°. What is the distance of the object from the point directly below the observer?

A) 25 meters B) 50 meters C) 50√3 meters D) 100 meters

14. If cos(theta) = 1/√2, what is the value of tan(theta) for an acute angle theta?

A) 1 B) √3 C) 1/√3 D) 2

15. What is the value of sec²(theta) - tan²(theta)?

A) 0 B) 1 C) -1 D) tan(theta)

16. If sin(theta) = 3/5 and theta is an acute angle, what is the value of tan(theta)?

A) 3/4 B) 4/3 C) 5/3 D) 5/4

17. The angle of elevation of the top of a tree from a point on the ground, which is 20 meters away from the foot of the tree, is 60°. What is the height of the tree?

A) 20√3 meters B) 20/√3 meters C) 40/√3 meters D) 40√3 meters

18. What is the value of sin(0°) + cos(0°)?

A) 0 B) 1 C) 2 D) -1

19. If tan(theta) = 1/√3, what is the value of sin(theta) for an acute angle theta?

A) 1/2 B) √3/2 C) 1/√2 D) 1

20. In a right-angled triangle, if tan(theta) = 7/24, what is the value of sin(theta)?

A) 7/25 B) 24/25 C) 7/12 D) 24/7

21. A kite is flying at a height of 60 meters above the ground. The string attached to the kite makes an angle of 60° with the horizontal. What is the length of the string?

A) 40√3 meters B) 40/√3 meters C) 60√3 meters D) 120/√3 meters

22. What is the value of (sin(theta) / cosec(theta)) + (cos(theta) / sec(theta))?

A) 1 B) 2 C) sin²(theta) D) cos²(theta)

23. If cosec(theta) = 5/3, what is the value of cot(theta) for an acute angle theta?

A) 3/4 B) 4/3 C) 5/3 D) 5/4

24. The angle of elevation of the top of a building from a point on the ground is 30°. If the distance from the point to the foot of the building is 30√3 meters, what is the height of the building?

A) 30 meters B) 60 meters C) 30√3 meters D) 90 meters

25. What is the value of tan(45°) * sin(90°)?

A) 0 B) 1 C) √3 D) 2

26. If sin(theta) = cos(theta), what is the value of theta in degrees?

A) 30° B) 45° C) 60° D) 90°

27. In a right-angled triangle, if sin(theta) = 8/17, what is the value of cos(theta)?

A) 8/17 B) 15/17 C) 17/8 D) 17/15

28. The angle of depression of a car from the top of a lighthouse 100 meters high is 60°. What is the distance of the car from the lighthouse?

A) 50 meters B) 100/√3 meters C) 100√3 meters D) 200/√3 meters

29. What is the value of (1 - sin²(theta)) / cos²(theta)?

A) 0 B) 1 C) tan²(theta) D) cot²(theta)

30. If tan(theta) = 5/12, what is the value of sec(theta) for an acute angle theta?

A) 12/13 B) 13/12 C) 5/13 D) 13/5

31. The angle of elevation of the top of a statue from a point on the ground 20 meters away from its base is 45°. What is the height of the statue?

A) 10 meters B) 20 meters C) 20√2 meters D) 40 meters

32. What is the value of sin(60°) * cos(30°)?

A) 1/2 B) 3/4 C) √3/2 D) 1

33. If cos(theta) = 1/2, what is the value of tan(theta) for an acute angle theta?

A) 1/√3 B) √3 C) 1 D) 2

34. In a right-angled triangle ABC, right-angled at B, if AC = 10 and angle A = 30°, what is the length of AB?

A) 5 B) 5√3 C) 10 D) 10√3

35. The angle of elevation of the top of a cliff from a boat is 30°. If the boat is 60√3 meters away from the cliff, what is the height of the cliff?

A) 30 meters B) 60 meters C) 60√3 meters D) 120 meters

36. What is the value of (sin(theta) + cos(theta))² - 2 sin(theta) cos(theta)?

A) 0 B) 1 C) 2 D) sin²(theta) + cos²(theta)

37. If cosec(theta) = 13/12, what is the value of cot(theta) for an acute angle theta?

A) 12/5 B) 5/12 C) 13/5 D) 5/13

38. The angle of depression of a car from the top of a tower is 30°. If the height of the tower is 75 meters, how far is the car from the tower?

A) 75/√3 meters B) 75√3 meters C) 150/√3 meters D) 150√3 meters

39. What is the value of tan(60°) / sin(60°)?

A) 1 B) 2 C) 2/√3 D) √3

40. If sin(theta) = 2/3, what is the value of cos(theta) for an acute angle theta?

A) √5/3 B) 3/√5 C) 2/√5 D) 3/2

41. In a right-angled triangle, the hypotenuse is 25 cm and one of the other sides is 7 cm. What is the sine of the angle opposite to the side of length 7 cm?

A) 7/25 B) 24/25 C) 7/24 D) 24/7

42. The angle of elevation of the top of a building from a point on the ground 50 meters away from its base is 60°. What is the height of the building?

A) 50/√3 meters B) 50√3 meters C) 100/√3 meters D) 100√3 meters

43. What is the value of sin(30°) + tan(45°)?

A) 1 B) 1.5 C) 2 D) 0.5

44. If tan(theta) = 3/4, what is the value of (sin(theta) + cos(theta)) / (sin(theta) - cos(theta))?

A) -7 B) 7 C) -1/7 D) 1/7

45. The angle of elevation of the top of a pole from a point 30 meters away from its foot is 30°. What is the height of the pole?

A) 15 meters B) 15√3 meters C) 30/√3 meters D) 30√3 meters

46. What is the value of (sec(theta) * sin(theta)) / tan(theta)?

A) 1 B) sin(theta) C) cos(theta) D) tan(theta)

47. If sin(theta) = 5/13, what is the value of tan(theta) for an acute angle theta?

A) 5/12 B) 12/5 C) 13/5 D) 13/12

48. A ladder 10 meters long reaches a window 8 meters above the ground. What is the angle of elevation of the ladder with the ground?

A) sin⁻¹(4/5) B) sin⁻¹(3/5) C) cos⁻¹(4/5) D) tan⁻¹(4/3)

49. What is the value of sin²(A) + cos²(A) + tan²(A) - sec²(A)?

A) 0 B) 1 C) -1 D) 2

50. If tan(theta) = 1, what is the value of (sin(theta) + cos(theta))²?

A) 1 B) 2 C) 3 D) 4

Trigonometric Ratios, Heights and Distances - Online Test

Test Results