SSC CAPFS and DP - complementary angles, heights and distances, applications of trigonometry Online Test (MCQ Quiz)

1. If two angles are complementary, their sum is:

A) 90 degrees B) 180 degrees C) 270 degrees D) 360 degrees

2. Which trigonometric ratio is used to find the height of an object when the angle of elevation and the distance from the object are known?

A) Sine B) Cosine C) Tangent D) Cotangent

3. The angle of elevation of the sun is 30 degrees. If the length of the shadow cast by a vertical pole is 45 meters, what is the height of the pole?

A) 15√3 meters B) 45/√3 meters C) 45 meters D) 30 meters

4. If angle A and angle B are complementary, and angle A = 40 degrees, what is the measure of angle B?

A) 40 degrees B) 50 degrees C) 90 degrees D) 140 degrees

5. In a right-angled triangle, if one of the non-right angles is θ, the other non-right angle is:

A) θ B) 90 - θ C) 180 - θ D) 90 + θ

6. What is the value of sin(30°)?

A) 1/2 B) √3/2 C) 1/√2 D) 1

7. What is the value of cos(60°)?

A) 1/2 B) √3/2 C) 1/√2 D) 0

8. What is the value of tan(45°)?

A) 0 B) 1/√3 C) 1 D) √3

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

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

10. Two angles are supplementary if their sum is:

A) 90 degrees B) 180 degrees C) 270 degrees D) 360 degrees

11. If tan(θ) = 3/4, what is the value of sin(θ) in a right-angled triangle?

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

12. A ladder of length 10 meters is leaning against a wall. If the foot of the ladder is 6 meters away from the base of the wall, what is the angle the ladder makes with the ground?

A) arcsin(3/5) B) arccos(3/5) C) arctan(3/5) D) arcsin(4/5)

13. If sin(θ) = 1/2, what is the value of θ?

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

14. The angle of depression of an object from a point is equal to the angle of elevation of the point from the object, provided the horizontal line is the same. This is a property related to:

A) Complementary angles B) Supplementary angles C) Alternate interior angles D) Corresponding angles

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

A) 40√3 meters B) 120/√3 meters C) 60 meters D) 80 meters

16. If cos(θ) = √3/2, what is the value of θ?

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

17. The angle of elevation of the top of a cliff from a boat is 30 degrees. If the boat sails 200 meters further away from the cliff, the angle of elevation becomes 15 degrees. What is the height of the cliff?

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

18. If tan(θ) = 1, what is the value of θ?

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

19. A vertical tree is broken by the wind. The broken part makes an angle of 30 degrees with the ground and touches the ground at a distance of 30 meters from the foot of the tree. What was the original height of the tree?

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

20. If sin(θ) = cos(θ), then θ is:

A) 0 degrees B) 30 degrees C) 45 degrees D) 60 degrees

21. The angle of elevation of the top of a tower from a point on the ground, which is 30 meters away from the foot of the tower, is 60 degrees. What is the height of the tower?

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

22. If angle A = 50 degrees and angle B = 40 degrees, then A and B are:

A) Complementary angles B) Supplementary angles C) Equal angles D) Adjacent angles

23. In a right-angled triangle ABC, with the right angle at B, if angle C = 30 degrees, then angle A is:

A) 30 degrees B) 60 degrees C) 90 degrees D) 120 degrees

24. What is the minimum height from which an object must be dropped so that its speed upon impact is 19.6 m/s? (g = 9.8 m/s²)

A) 9.8 meters B) 19.6 meters C) 29.4 meters D) 39.2 meters

25. If tan(A) = cot(B), then A + B is equal to:

A) 90 degrees B) 180 degrees C) 270 degrees D) 360 degrees

26. A bird is sitting on the top of a tree 15 meters high. It flies off and lands on the ground at a point 20 meters away from the base of the tree. What is the angle of depression from the bird's initial position to the landing spot?

A) arctan(3/4) B) arctan(4/3) C) arcsin(3/5) D) arccos(3/5)

27. If sin(θ) = 3/5, what is the value of cos(θ) in a right-angled triangle?

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

28. The angle of elevation of the top of a building from a point P on the ground is 30 degrees. If the point P is moved 20 meters closer to the building, the angle of elevation becomes 60 degrees. What is the height of the building?

A) 10√3 meters B) 20√3 meters C) 30 meters D) 30√3 meters

29. If two angles are supplementary and one is twice the other, what are the angles?

A) 30° and 60° B) 45° and 90° C) 60° and 120° D) 90° and 90°

30. What is the value of sin²(θ) + cos²(θ)?

A) 0 B) 1 C) sin(θ) D) cos(θ)

31. A man stands 100 meters away from a lighthouse. The angle of elevation of the top of the lighthouse from the man's eyes is 30 degrees. If the man's height is 1.5 meters, what is the height of the lighthouse?

A) 100/√3 + 1.5 meters B) 100√3 + 1.5 meters C) 50√3 + 1.5 meters D) 50/√3 + 1.5 meters

32. If cot(θ) = 5/12, what is the value of cosec(θ) in a right-angled triangle?

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

33. The angle of elevation of the top of a tower from a point A on the ground is 45 degrees. From another point B, 10 meters above A and on the line joining A to the foot of the tower, the angle of elevation is 60 degrees. What is the height of the tower?

A) 10(√3 + 1) meters B) 10(√3 - 1) meters C) 5(√3 + 1) meters D) 5(√3 - 1) meters

34. If sec(θ) = 13/5, what is the value of tan(θ) in a right-angled triangle?

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

35. A balloon is observed from two points on the ground, diametrically opposite to each other, on a straight road passing below the balloon. The angles of elevation are 30 degrees and 60 degrees. If the height of the balloon is 100 meters, what is the distance between the two points?

A) 100(√3 + 1/√3) meters B) 100(√3 - 1/√3) meters C) 100(1/√3 + √3) meters D) 100(1/√3 - √3) meters

36. What is the value of sin(90° - θ)?

A) sin(θ) B) cos(θ) C) -sin(θ) D) -cos(θ)

37. If the angle of elevation of the sun increases from 30 degrees to 60 degrees, the length of the shadow of a vertical pole:

A) Increases B) Decreases C) Remains the same D) Becomes zero

38. A flagstaff stands on the top of a building. At a point on the ground 20 meters away from the base of the building, the angle of elevation of the top of the flagstaff is 60 degrees and the angle of elevation of the base of the flagstaff is 45 degrees. What is the height of the flagstaff?

A) 20(√3 - 1) meters B) 20(√3 + 1) meters C) 10(√3 - 1) meters D) 10(√3 + 1) meters

39. If tan(θ) = 1/√3, what is the value of θ?

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

40. Two observers are on the same side of a tower, at distances x and y (y > x) from its base. The angles of elevation of the top of the tower are α and β respectively. If x = 100m and y = 200m, and α = 60°, what is β?

A) arctan(√3/2) B) arctan(√3) C) arctan(1/√3) D) arctan(2/√3)

41. What is the value of cos(90° - θ)?

A) sin(θ) B) cos(θ) C) -sin(θ) D) -cos(θ)

42. A man can see the top of a tower at an angle of elevation of 30 degrees. If he walks towards the tower a distance of 100 meters, the angle of elevation becomes 60 degrees. What is the initial distance of the man from the tower?

A) 100 meters B) 150 meters C) 200 meters D) 250 meters

43. If A and B are complementary angles, then which of the following is true?

A) tan(A) = tan(B) B) sin(A) = cos(B) C) cos(A) = sin(B) D) tan(A) = cot(B)

44. A vertical pole of length 6 meters casts a shadow of length 4 meters when the sun's altitude is θ. What is the value of tan(θ)?

A) 2/3 B) 3/2 C) 4/6 D) 6/4

45. If the angle of elevation of the sun is 30 degrees, the ratio of the height of a vertical object to the length of its shadow is:

A) 1 : √3 B) √3 : 1 C) 1 : 2 D) 2 : 1

46. From the top of a cliff 100 meters high, the angle of depression of a boat is 30 degrees. How far is the boat from the foot of the cliff?

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

47. If tan(θ) = 5/12, what is the value of sin(θ) + cos(θ)?

A) 17/13 B) 13/17 C) 17/5 D) 5/17

48. Two persons are on opposite sides of a tower 100 m high. They observe the angle of elevation of the top of the tower to be 30 degrees and 45 degrees respectively. What is the distance between the two persons?

A) 100(√3 + 1) meters B) 100(√3 - 1) meters C) 100(1 + 1/√3) meters D) 100(1 - 1/√3) meters

49. If sin(2θ) = cos(θ), and 2θ and θ are acute angles, then θ is:

A) 15 degrees B) 30 degrees C) 45 degrees D) 60 degrees

50. A boy is flying a kite. The string of the kite is 150 meters long. The angle of elevation of the kite from the boy's hand is 60 degrees. If the boy's hand is 1 meter above the ground, what is the height of the kite from the ground?

A) 150√3 + 1 meters B) 75√3 + 1 meters C) 75√3 meters D) 150√3 meters

complementary angles, heights and distances, applications of trigonometry - Online Test

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