# MCQs for Class 10 Maths Chapter 9 Applications of Trigonometry

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1. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun

(a) is also increasing

(b) is decreasing

(c) remains unaffected

(d) Don’t have any relation with length of shadow

Answer: (b) is decreasing

2. The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

(a)10 m

(b)30/√3 m

(c)√3/10 m

(d)30 m

Answer: (b)30/√3 m

3. If at some time, the length of the shadow of a tower is √3 times its height, then the angle of elevation of the sun, at that time is:

(a) 15°

(b) 30°

(c) 45°

(d) 60°

Answer: (b) 30°

4. The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Answer: (b) 45°

5. If the altitude of the sun is 60°, the height of a tower which casts a shadow of length 90m is

(a) 60m

(b) 90m

(c) 60√3m

(d) 90√3m

Answer:(d) 90√3m

6. The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is

(a) √3 m

(b) 2√3 m

(c) 5√3m

(d) 10√3 m

Answer: (d) 10√3 m

7. The **_** of an object is the angle formed by the line of sight with the horizontal when the object is below the horizontal level.

(a) line of sight

(b) angle of elevation

(c) angle of depression

(d) none of these

Answer: (c) angle of depression

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8. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will

(a) also get doubled

(b) will get halved

(c) will be less than 60 degree

(d) None of these

Answer: (c) will be less than 60 degree

9. If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:

(a)Increases

(b)Decreases

(c)Do not change

(d)None of the above

Answer: (c)Do not change

10. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is:

(a) 15√3 m

(b) 15√3/2 m

(c) 15/2 m

(d) 15 m

Answer: (c) 15/2 m

11. A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is

(a) 6√3 m

(b) 4√3 m

(c) 3√3 m

(d) 2√3 m

Answer: (a) 6√3 m

12. The top of a broken tree has its top touching the ground at a distance of 10m from the bottom. If the angle made by the broken part with the ground is 30°, then the length of the broken part is

(a) 20m

(b) 20√3m

(c) 10√3m

(d) 20/√3m

Answer: (d) 20/√3m

13. The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is

(a) 10√33 m

(b) 5√33 m

(c) √3 m

(d) √3/5 m

Answer: (b) 5√33 m

14. When the sun’s altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

(a) 35 m

(b) 140 m

(c) 60.6 m

(d) 20.2 m

Answer: (c) 60.6 m

15. If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top

(a) increases

(b) decreases

(c) remains unchanged

(d) have no relation.

Answer: (c) remains unchanged

16. If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:

(a)60°

(b)45°

(c)30°

(d)90°

Answer: (a)60°

17. At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is:

(a) 30°

(b) 60°

(c) 90°

(d) 45°

Answer: (d) 45°

18. The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is

(a) 50 m

(b) 150 m

(c) 50√3m

(d) 50(3 + √3)

Answer: (d) 50(3 + √3)

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19. If a kite is flying at a height of 10√3m from the level ground attached to a string inclined at 60° to the horizontal then the length of the string is

(a) 20m

(b) 40√3m

(c) 60√3m

(d) 80√3m

►Answer:(a) 20m

20. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is

(a) 6 m

(b) 10 m

(c) 12 m

(d) 20 m

Answer: (c) 12 m

21. A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45o. The height of the tower will be

(a) 30√3 m

(b) 40√3 m

(c) 30 m

(d) 40 m

Answer: (c) 30 m

22. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be

(a) 7.5m

(b) 7.7m

(c) 8.5m

(d) 8.8m

Answer: (a) 7.5m

23. The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

(a)10√3 m

(b)15√3 m

(c)12√3 m

(d)36 m

Answer: (a)10√3 m

24. A person is flying a kite at a height of 30 m from the horizontal level. The length of string from the kite to the person is 60 m. Assuming that here is no slack in the string, the angle of elevation of kite to the horizontal level is:

(a) 45°

(b) 30°

(c) 60°

(d) 90°

Answer: (b) 30°

25. The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 30° at a point 8m from the foot of the tree. The original height of the tree is

(a) 8m

(b) 24m

(c) 24√3m

(d) 8√3m

Answer: (d) 8√3m

26. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m) is:

(a) 25√3

(b) 50√3

(c) 75√3

(d) 150

Answer: (c) 75√3

27. From a point P on the level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100m high, the distance between P and the foot of the tower is

(a) 100√3m

(b) 200√3m

(c) 300√3m

(d) 150√3m

Answer: (a) 100√3m

28. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high.Determine the angle of elevation of the top of the tower from the eye of the observer.

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Answer: (b) 45°

29. The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called:

(a)Angle of elevation

(b)Angle of depression

(c)No such angle is formed

(d)None of the above

Answer: (b)Angle of depression

30. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of tower (in m) is:

(a) 25√3

(b) 50√3

(c) 75√3

(d) 150

Answer: (c) 75√3

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31. If the length of a shadow of a tower is increasing, then the angle of elevation of the sun is

(a) neither increasing nor decreasing

(b) decreasing

(c) increasing

(d) none of these

Answer:(b) decreasing

32. The line drawn from the eye of an observer to the point in the object viewed by the observer is known as

(a) horizontal line

(b) vertical line

(c) line of sight

(d) transversal line

Answer: (c) line of sight

33. The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:

(a) 45°

(b) 60°

(c) 30°

(d) None of these

Answer:(a) 45°

34. The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is:

(a) st

(b) s^{2}t^{2}

(c) √st

(d) s/t

Answer: (c) √st

35. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:

(a)Angle of elevation

(b)Angle of depression

(c)No such angle is formed

(d)None of the above

Answer: (a)Angle of elevation

36. A man at the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance travelled by the car during this time interval is:

(a) 10√3 m

(b) 100√3/3 m

(c) 200√3/3 m

(d) 200√3 m

Answer: (c) 200√3/3 m

37. An electric pole is 10√3 m high and its shadow is 10m in length, then the angle of elevation of the sun is

(a) 15°

(b) 30°

(c) 45°

(d) 60°

Answer: (d) 60°

38.If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1 : h2 =

(a) 1 : 2

(b) 1 : 3

(c) 2 : 1

(d) 3 : 1

Answer: (d) 3 : 1

39. When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is

(a) 30°

(b) 45°

(c) 60°

(d) 15°

Answer: (a) 30°

40. The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Then the height of tower is:

(a) 20√3

(b) 25√3

(c) 10√3

(d) 30√3

Answer: (b) 25√3

41. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower standing straight is:

(a)15√3

(b)10√3

(c)12√3

(d)20√3

Answer: (a)15√3

42. The angle of elevation of the top of a 15 m high tower at a point 15 m away from the base of tower is:

(a) 30°

(b) 60°

(c) 45°

(d) 75°

Answer: (c) 45°

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43. A man standing at a height 6 m observes the top of a tower and the foot of tower at angles of 45° and 30° of elevation and depression respectively. The height of tower is:

(a) 6√3 m

(b) 12 m

(c) 6(√3 – 1)

(d) 6(√3 + 1) m

Answer: (d) 6(√3 + 1) m

44. The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45^{o}. Which equation can be used to find the height of the pole.

(a) cos 45° = h/30

(b) tan 45° = 30/h

(c) tan 45° = h/30

(d) sin 45° = h/30

►Answer:(c) tan 45° = h/30

45. Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is

(a) 5 m

(b) 8 m

(c) 9 m

(d) 10 m

Answer: (c) 9 m

46. A contractor planned to install a slide for the children to play in a park. If he prefers to have a slide whose top is at a height of 1.5m and is inclined at an angle of 30° to the ground, then the length of the slide would be

(a) 1.5m

(b) 2√3m

(c) √3m

(d) 3m

Answer: (d) 3m

47. If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is

(a) equal to the angle of depression of its reflection.

(b) double to the angle of depression of its reflection

(c) not equal to the angle of depression of its reflection

(d) information insufficient

Answer: (c) not equal to the angle of depression of its reflection

48. The height or length of an object or the distance between two distant objects can be determined with the help of:

(a)Trigonometry angles

(b)Trigonometry ratios

(c)Trigonometry identities

(d)None of the above

Answer: (b)Trigonometry ratios

49. Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is:

(a) 5 m

(b) 8 m

(c) 9 m

(d) 10 m

Answer: (d) 10 m

50. A kite is flying at a height of 60m from the level ground, attached to a string inclined at 30° to the horizontal. The length of the string is

(a) 60m

(b) 120m

(c) 40√3m

(d) 60√3m

Answer:(b) 120m

51. A portion of a 60 m long tree is broken by tornado and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to

(a) 30 m

(b) 35 m

(c) 40 m

(d) 20 m

Answer:(d) 20 m

52. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. If the angle made by the rope with the ground level is 30°, then the height of the pole is

(a) 10m

(b) 20m

(c) 10√3m

(d) 20√3m

Answer: (a) 10m

53. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Answer: (a) 60°

54. A 6 feet tall man finds that the angle of elevation of a 24 feet high pillar and the angle of depression of its base are complementary angles. The distance of man from the pillar is:

(a) 4√3 feet

(b) 6√3 feet

(c) 8√3 feet

(d) 10√3 feet

Answer: (b) 6√3 feet

55. If altitude of the sun is 60°, the height of a tower which casts a shadow of length 30m is

(a) 10√3m

(b) 15√3m

(c) 20√3m

(d) 30√3m

Answer: (d) 30√3m

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56. The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is

(a) √3 m

(b) 2√3 m

(c) 5√3m

(d) 10√3 m

Answer :(d) 10√3 m

57. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower

(a) 10 (√3 + 1)

(b) 5√3

(c) 5 (√3 + 1)

(d) 10√3

Answer:(a) 10 (√3 + 1)

58. A lamp post 5√3 m high casts a shadow 5 m long on the ground. The sun’s elevation at this point is:

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Answer: (c) 60°

59. The angle of elevation from a point 30 metre from the base of tree as level ground to the top of the tree is 60°. The height of the tree is :

(a) 60√3 m

(b) 30√3 m

(c) 30 m

(d) 30/√3 m

Answer: (b) 30√3 m

60. A circus artist is climbing a long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The ratio of the height of the pole to the length of the string is 1 :√2. The angle made by the rope with the ground level is

(a) 30°

(b) 45°

(c) 60°

(d) none of these

Answer: (b) 45°

61. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is:

(a) 10√3 m

(b) 15√3 m

(c) 12√3 m

(d) 36 m

Answer: (a) 10√3 m

62. The angle of elevation of the top of a tower from a point P on the ground is α. After walking α distance d towards the foot of the tower, angle of elevation is found to be β. Then

(a) α < β

(b) α > β

(c) α = β

(d) None of these

Answer: (a) α < β

63. A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. What is the height of the hill?

(a) 8√3 m

(b) 24 m

(c) 32 m

(d) 24√3 m

Answer:(c) 32 m

64. If sun’s elevation is 60° then a pole of height 6 m will cast a shadow of length

(a) 3√2 m

(b) 6√3 m

(c) 2√3 m

(d) √3 m

Answer: (c) 2√3 m

65. The angle of elevation of the top of a vertical tower from a point on the ground is60°. From another point 10 m vertically above the first, its angle of elevation is45°. Find the height of the tower.

(a) 5 (√3 + 3) m

(b) (√3 +3) m

(c) 15 (√3 +3)

(d) 5√3

Answer: (a) 5 (√3 + 3) m

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66. If the angles of elevation of the top of a tower from two points at the distance of 3 m and 12 m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is:

(a) 36

(b) 60

(c) 6

(d) 100

Answer: (c) 6

67. A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45°. The height of the tree is:

(a) 5.2 m

(b) 4 m

(c) 3 m

(d) 4.5 m

Answer: (b) 4 m

68. A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal is

(a) 450

(b) 300

(c) 900

(d) 600

Answer: (b) 300

69. There are two windows in a house. A window of the house is at a height of 1.5 m above the ground and the other window is 3 m vertically above the lower window. Ram and Shyam are sitting inside the two windows. At an instant, the angle of elevation of a balloon from these windows are observed as 45° and 30° respectively. Find the height of the balloon from the ground.

(a) 7.598m

(b) 8.269m

(c) 7.269m

(d) 8.598 m

Answer: (d) 8.598 m

70. An electric pole is tied from the top to a point (some distance away from the base) on the ground using a string. The ratio of the height of pole to the string is √3 : 2, then the angle of elevation of the top from the point on the ground is

(a) 30°

(b) 45°

(c) 60°

(d) none of these

►Answer:(c) 60°

71. A tower stands vertically on the ground. From a point C on the ground, which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 450. The height of the tower is

(a) 15 m

(b) 8 m

(c) 20 m

(d) 10 m

Answer: (a) 20 m

72. A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of ladder is 8 m away from the wall, the length of ladder is:

(a) 4 m

(b) 8 m

(c) 8√2 m

(d) 16 m

Answer: (d) 16 m

73. If the length of the shadow of a tower is equal to its height, then the angle of elevation of the sun is

(a) 30°

(b) 45°

(c) 60°

(d) 65°

Answer: (b) 45°

74. A bridge, in the shape of a straight path across a river, makes an angle of 60° with the width of the river. If the length of the bridge is 100 m, then the width of the river is:

(a) 50 m

(b) 173.2 m

(c) 43.3 m

(d) 100 m

Answer: (a) 50 m

75.Guddi was standing on a road near a mall. She was 1000m away from the mall and able to see the top of the mall from the road in such a way that top of the tree, which is in between her and the mall, was exactly in line of sight with the top of the mall. The tree height is 10m and it is 20m away from Guddi. How tall is the mall?

(a) 453m

(b) 856m

(c) 290m

(d) 470m

Answer: (d) 470m

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