Height and Distance in Aptitude MCQ Questions and Answers

1. A man 2 m tall is walking away from a lamp-post 6 m high. When he is 10 m from the lamp-post, the length of his shadow is:
A) 2 m
B) 5 m
C) 3 m
D) 4 m
Answer: B) 5 m

2. From a point on the ground, the angle of elevation of the top of a vertical tower is 30°. If the height of the tower is 100 m, the horizontal distance from the point to the tower (approx.) is:
A) 100 m
B) 173.21 m
C) 57.74 m
D) 200 m
Answer: B) 173.21 m

3. Two towers are 100 m apart. From a point on the ground between them, the angles of elevation to their tops are 60° and 30° respectively. If the heights of the towers are equal, the height of each tower is:
A) 86.6 m
B) 100 m
C) 50 m
D) 173.2 m
Answer: A) 86.6 m

4. A 10 m ladder leans against a wall making an angle of 60° with the ground. The height reached on the wall is:
A) 5 m
B) 8.66 m
C) 10 m
D) 6 m
Answer: B) 8.66 m

5. From a point 50 m away from the base of a tower, the angle of elevation of the top is 45°. The height of the tower is:
A) 35.36 m
B) 50 m
C) 50 m
D) 70.71 m
Answer: C) 50 m

6. If the angle of elevation of the top of a tower from two points on the same straight line with the tower are 30° and 60°, and the two points are 30 m apart, the height of the tower is:
A) 10 m
B) 17.32 m
C) 20 m
D) 30 m
Answer: B) 17.32 m

7. A man 1.8 m tall casts a shadow 3 m long. The angle of elevation of the sun is:
A) 30°
B) 30.96°
C) 36.87°
D) 45°
Answer: B) 30.96°

8. From the top of a 20 m tower, the angle of depression of a car on the road is 30°. The distance of the car from the base is:
A) 10 m
B) 34.64 m
C) 34.64 m
D) 11.55 m
Answer: C) 34.64 m

9. Two poles of heights 15 m and 20 m are 25 m apart. The angle of elevation of the top of the taller pole from the base of the shorter is approximately:
A) 53.13°
B) 36.87°
C) 33.69°
D) 40°
Answer: C) 33.69°

10. A ship is observed from the top of a lighthouse 30 m high at an angle of depression of 15°. The distance of the ship from the lighthouse base is approximately:
A) 115.77 m
B) 114.3 m
C) 103.92 m
D) 120 m
Answer: B) 114.3 m

11. From a point 40 m from the base of a building, angle of elevation of its top is 60°. Height of building is:
A) 40 m
B) 69.28 m
C) 23.09 m
D) 80 m
Answer: B) 69.28 m

12. Two towers are 150 m apart. From a point between them, angles of elevation to their tops are equal at 45°. If the point is x meters from the first tower, heights of towers will be:
A) x and 150−x
B) x and 150−x (same heights so x = 75)
C) both 75 m
D) cannot be equal unless x = 75
Answer: B) x and 150−x (same heights so x = 75)

13. The angle of elevation of the top of a pole from two points at distances 20 m and 45 m from its base are 60° and 30° respectively. The height of the pole is:
A) 10√3 m
B) 20√3 m
C) 15√3 m
D) 5√3 m
Answer: B) 20√3 m

14. From a boat, the angles of elevation to the top and bottom of a vertical mast on a ship are 60° and 45° respectively. If the mast height is H, the horizontal distance from the boat to the ship is:
A) H/√3
B) H/√3
C) H
D) √3 H
Answer: B) H/√3

15. A man observes the top of a tower at an angle of elevation 45°. He walks 20 m towards it and angle becomes 60°. Height of tower is:
A) 20(√3+1) m
B) 20(√3+1) m
C) 40 m
D) 20 m
Answer: B) 20(√3+1) m

16. From the top of a 50 m building, angle of depression of a car is 30°. How far is the car from the building?
A) 86.6 m
B) 86.6 m
C) 28.87 m
D) 50 m
Answer: B) 86.6 m

17. Two towers are of equal height. A person standing at a point sees their tops under angles 30° and 60°. The point lies on the line joining the bases. If distance between towers is 40 m, the height of each tower is:
A) 23.09 m
B) 23.09 m
C) 20 m
D) 40 m
Answer: B) 23.09 m

18. A flagstaff 12 m high casts a shadow of 16 m. The angle of elevation of the sun is:
A) 36.87°
B) 45°
C) 30°
D) 53.13°
Answer: A) 36.87°

19. A tree 20 m tall casts a shadow of 10 m. What is the angle of elevation of the sun?
A) 30°
B) 63.43°
C) 45°
D) 26.57°
Answer: B) 63.43°

20. From a point on ground the angles of elevation of top and bottom of a window of a building are 45° and 60° respectively. If the window height is 3 m, distance from the point to building is:
A) 3(√3−1) m
B) 3(√3−1) m
C) 2 m
D) 4 m
Answer: B) 3(√3−1) m

21. A man 1.5 m tall stands 10 m away from a vertical wall. Angle of elevation of top of wall from top of man’s head is 30°. Height of wall is:
A) 9.66 m
B) 10.16 m
C) 12.5 m
D) 8 m
Answer: B) 10.16 m

22. From a point P, the angles of elevation of two towers A and B are 45° and 30°. Distance between the towers is 100 m and P is nearer to A. Height of A minus height of B is:
A) 0
B) 20 m
C) (100(1−1/√3)) m ≈ 42.13 m
D) 50 m
Answer: C) (100(1−1/√3)) m ≈ 42.13 m

23. A pole of 8 m casts a shadow 6 m long. Height of a building casting shadow 15 m at same time is:
A) 16 m
B) 20 m
C) 18 m
D) 10 m
Answer: B) 20 m

24. From two points 50 m and 100 m away from a tower on same side, the angles of elevation of the top are α and β respectively. If tan α = 2 tan β, height of tower is:
A) 50√2 m
B) 50(2−1) m (depends on numeric — correct derivation needed)
C) 100 m
D) 50 m
Answer: B) 50(2−1) m (depends on numeric — correct derivation needed)

25. From the top of a 45 m building, the angles of depression of two cars are 30° and 60°. The distance between the cars along the ground is:
A) 45(√3−1) m
B) 45(√3−1) m
C) 45 m
D) 90 m
Answer: B) 45(√3−1) m

26. A 15 m pole and a 20 m pole stand vertically 30 m apart. From a point on the line joining the bases, the angles of elevation to the tops are equal. Distance of the point from the shorter pole is:
A) 18 m
B) 12 m
C) 15 m
D) 10 m
Answer: A) 18 m

27. Observer O is 50 m from a tower. Angle of elevation of top is 53.13°. Height of tower is:
A) 40 m
B) 66.66 m
C) 45 m
D) 25 m
Answer: B) 66.66 m

28. From two points 40 m apart, bearings of a tower are such that angles of elevation from nearer and farther points are 60° and 30°. Height of tower is:
A) 23.09 m
B) 40 m
C) 46.18 m
D) 20 m
Answer: A) 23.09 m

29. A man looks at top of a building at 45° angle. Walking 10 m towards building, angle becomes 60°. Height of building is:
A) 10(√3+1) m
B) 10(√3+1) m
C) 20 m
D) 5 m
Answer: B) 10(√3+1) m

30. A balloon is rising vertically and at some instant its angle of elevation from a point is 30°. After 10 seconds the angle becomes 60°. If the point is 100 m from the vertical path, the distance the balloon rose in 10 s is:
A) 100(√3−1) m
B) 100(√3−1) m
C) 50 m
D) 173.2 m
Answer: B) 100(√3−1) m

31. A man 2 m tall is walking away from a lamppost 10 m high. When he is 15 m from the lamppost, length of his shadow is:
A) 7.5 m
B) 3.75 m
C) 5 m
D) 2.5 m
Answer: B) 3.75 m

32. From the top of a cliff 80 m high, the angle of depression of a boat is 30°. Distance of boat from cliff base:
A) 138.56 m
B) 100 m
C) 80 m
D) 46.19 m
Answer: A) 138.56 m

33. Two buildings of heights 40 m and 60 m stand 50 m apart. Angle of elevation to the top of taller building from base of shorter building is:
A) 53.13°
B) 50.19°
C) 36.87°
D) 60°
Answer: B) 50.19°

34. A ladder 13 m long reaches a window 12 m high. Angle ladder makes with ground is:
A) 67.38°
B) 30°
C) 60°
D) 55°
Answer: A) 67.38°

35. From a point on the ground, the angle of elevation of the top of a pole is 30°. On moving 40 m towards it, angle becomes 60°. Height of pole:
A) 40√3 m
B) 40√3 m
C) 80 m
D) 20 m
Answer: B) 40√3 m

36. From a point, top of tower is seen at 60°; moving 10 m closer, angle becomes 75°. If height is h, the horizontal distances satisfy: tan60 = h/d and tan75 = h/(d−10). Solve for h when possible. Which expression gives h?
A) 10(tan60 tan75)/(tan75−tan60)
B) 10·(tan60·tan75)/(tan75−tan60)
C) 10/(tan75−tan60)
D) none of these
Answer: B) 10·(tan60·tan75)/(tan75−tan60)

37. A wire from top of a pole of height 10 m is tied to a point on ground 5 m from base. The angle between wire and ground is:
A) 63.43°
B) 63.43°
C) 45°
D) 30°
Answer: B) 63.43°

38. Two poles 20 m and 15 m high stand 24 m apart. From a point on ground on the line joining the poles, angles of elevation to their tops are equal. Distance of the point from the smaller pole is:
A) 14.4 m
B) 9.6 m
C) 12 m
D) 10 m
Answer: B) 9.6 m

39. From the top of a 60 m tower, the angle of depression of a car is 36.87°. Distance of car from base is:
A) 80 m
B) 80 m
C) 100 m
D) 60 m
Answer: B) 80 m

40. Angle of elevation of top of a tree from two points on same side are complementary. If distances are 30 m and 40 m, height of tree is:
A) 24 m
B) 24 m
C) 20 m
D) 30 m
Answer: B) 24 m

41. A man is 1.6 m tall and stands 6 m from a wall. The angle of elevation of the top of a poster on the wall from his eyes is 45°. Height of poster from ground is:
A) 7.6 m
B) 7.6 m
C) 5 m
D) 8 m
Answer: B) 7.6 m

42. From a point, angle of elevation of top of tower is 30°. After moving 10 m closer, angle is 45°. Height of tower is:
A) 10(√3+1) m
B) 20 m
C) 10 m
D) 5(√3+1) m
Answer: A) 10(√3+1) m

43. Two ships are sailing west and east respectively. From a point on shore the angles of elevation to their masts are equal; the nearer ship is 100 m away. If heights of masts are same, distance to farther ship is:
A) 100 m
B) 100 m
C) cannot be determined
D) 200 m
Answer: B) 100 m

44. A man walking towards a tower notices that the angle of elevation increases from 30° to 45° after 10 m. Height of tower:
A) 10(√3+1) m
B) 10(√3+1) m
C) 20 m
D) 5 m
Answer: B) 10(√3+1) m

45. From a point 80 m away, top of tower is at 36.87°. Height of tower is:
A) 48 m
B) 48 m
C) 60 m
D) 40 m
Answer: B) 48 m

46. A pole casts a shadow 4 m long when the sun’s elevation is 53.13°. Height of pole:
A) 5.333 m
B) 4 m
C) 6 m
D) 3 m
Answer: A) 5.333 m

47. Two towers standing opposite each other across a road 30 m wide have heights 25 m and 15 m. From a point on the road directly between bases, angle of elevation to taller tower’s top is:
A) 39.81°
B) 26.57°
C) 33.69°
D) 45°
Answer: A) 39.81°

48. Observer at top of one tower 20 m high sees top of another tower at angle of depression 15°. If towers are on same level, distance between towers is:
A) 73.15 m
B) 40 m
C) 115.47 m
D) 35 m
Answer: A) 73.15 m

49. From a point on the ground, top of a pole is seen at angle θ. On moving 5 m towards it, the angle becomes 2θ. If initial distance is d, relation between d and θ is:
A) tan θ = h/d, tan 2θ = h/(d−5)
B) tan θ = h/d, tan 2θ = h/(d−5)
C) tan θ = d/h
D) none of these
Answer: B) tan θ = h/d, tan 2θ = h/(d−5)

50. A vertical pole and its shadow make an angle of 60° with the ground. If the pole is 10 m high, length of shadow is:
A) 5.77 m
B) 5.77 m
C) 10 m
D) 20 m
Answer: B) 5.77 m

51. A man 1.75 m tall observes the top of a tower at an angle of 53.13°. Distance from man to tower is 10 m. Height of tower approximately:
A) 20 m
B) 20.75 m
C) 10 m
D) 18 m
Answer: B) 20.75 m

52. Two vertical poles of equal height cast shadows 10 m and 15 m long. Ratio of heights equals ratio of:
A) 10:15
B) 15:10
C) 1:1
D) cannot be determined
Answer: A) 10:15

53. From two points A and B on same side of a tower, angles of elevation are 30° and 45°; AB = 20 m, A nearer. Height of tower:
A) 20(√3+1)/ (√3) m
B) 20 m
C) 10 m
D) 40 m
Answer: A) 20(√3+1)/ (√3) m

54. A man stands at distance x from a pole and sees the top at an angle of 45°. If he steps back 10 m, angle reduces to 30°. What is x?
A) 10(√3+1) m
B) 10(√3+1) m
C) 20 m
D) 5 m
Answer: B) 10(√3+1) m

55. From a point on the ground the angles of elevation of top and bottom of a window are 60° and 30°. If the bottom is at 3 m height, the top is at:
A) 3 + 3√3 m
B) 3 + 3√3 m
C) 6 m
D) 3√3 m
Answer: B) 3 + 3√3 m

56. A balloon rising vertically is observed from two points on the ground 120 m apart. Angles of elevation are 30° and 60°. Height of balloon:
A) 69.28 m
B) 69.28 m
C) 120 m
D) 40 m
Answer: B) 69.28 m

57. A man 1.6 m tall standing 8 m from a pole sees its top at 60°. Height of pole is:
A) 15.33 m
B) 10 m
C) 14 m
D) 13 m
Answer: A) 15.33 m

58. From the top of a 30 m tower, the angle of depression of a car is 37°. Distance between car and tower base approx:
A) 40 m
B) 30 m
C) 50 m
D) 60 m
Answer: A) 40 m

59. A kite is flying 80 m above ground attached to string making angle 60° with ground. Length of string is:
A) 160 m
B) 92.38 m
C) 80 m
D) 46.19 m
Answer: B) 92.38 m

60. A tower casts a shadow of 12 m. When sun rises, shadow decreases to 6 m. Ratio of heights? (Heights unchanged — trick: same pole)
A) 1:2
B) 1:1
C) 2:1
D) cannot be determined
Answer: B) 1:1

61. From a point 30 m from a building base, angle of elevation to the top is 60°. If a 2 m man standing at the same point sees the top at 58.5°, approximate height of building:
A) 51.96 m
B) 51.96 m
C) 53 m
D) 50 m
Answer: B) 51.96 m

62. Two poles of heights 9 m and 12 m are 15 m apart. A point is such that angles to their tops are equal. Distance from taller pole is:
A) 9 m
B) 6 m
C) 7.5 m
D) 5 m
Answer: A) 9 m
63. From a point, angle of elevation of top of tower is 30°. If the tower height doubles, the new angle of elevation from same point:
A) remains 30°
B) increases (>30°)
C) decreases
D) becomes 60°
Answer: B) increases (>30°)

64. Observer at point P sees top of a tower under 45°. P is 40 m from base. Height of tower:
A) 40 m
B) 28.87 m
C) 56.57 m
D) 20 m
Answer: A) 40 m

65. From the top of a hill 100 m high, angle of depression to a car is 30°. Horizontal distance is:
A) 173.2 m
B) 173.2 m
C) 100 m
D) 57.7 m
Answer: B) 173.2 m

66. A person 1.7 m tall standing 5 m from a wall sees top of the wall at angle 53.13°. Height of wall:
A) 6.85 m
B) 5 m
C) 7.5 m
D) 10 m
Answer: A) 6.85 m

67. Two towers of equal height stand 80 m apart. From a point midway between them, angle of elevation to their tops is 45°. Height is:
A) 40 m
B) 56.57 m
C) 80 m
D) 28.87 m
Answer: A) 40 m

68. A man moving away from a lamp post notices his shadow increasing at constant rate. At a certain moment his distance from lamp is doubled, his shadow length:
A) halves
B) more than doubles
C) doubles
D) cannot say
Answer: B) more than doubles

69. A vertical pole and a vertical building cast shadows of lengths 4 m and 16 m respectively at same time. Height of building is 48 m. Height of pole:
A) 12 m
B) 12 m
C) 16 m
D) 8 m
Answer: B) 12 m

70. From a point between two towers 80 m apart, angles of elevation are 45° and 60° to the nearer and farther towers respectively. Distance from nearer tower is:
A) 20 m
B) 32 m
C) 40 m
D) 48 m
Answer: B) 32 m

71. A man 1.5 m tall stands 20 m from a wall. The angle of elevation of top of the wall from his eyes is 30°. Height of wall:
A) 12.98 m
B) 18.98 m
C) 20 m
D) 10 m
Answer: B) 18.98 m

72. From a point on ground angle of elevation to top of tower is 15°. After moving 150 m towards tower, angle becomes 30°. Height of tower:
A) 150√3/ (√3−1) m
B) 150×tan30×tan15/(tan30−tan15) (expression form)
C) 100 m
D) 200 m
Answer: B) 150×tan30×tan15/(tan30−tan15)

73. Two towers A and B are 60 m and 80 m high and are 100 m apart. From centre point between them, angle of elevation to A and B are:
A) equal
B) not equal
C) both 45°
D) both 30°
Answer: B) not equal

74. A light is at top of a pole 8 m high. A 1.6 m person is 12 m away. How long is shadow of person when light rays are straight?
A) 2.4 m
B) 2.4 m
C) 3 m
D) 4 m
Answer: B) 2.4 m

75. From top of a cliff height 200 m, angle of depression of boat is 10°. Distance from base:
A) 1119.54 m
B) 200 m
C) 1000 m
D) 400 m
Answer: A) 1119.54 m

76. A vertical pole of height h casts a shadow s when sun’s elevation is θ. Relationship:
A) tan θ = h/s
B) tan θ = h/s
C) h = s tan θ
D) both B and C equivalent
Answer: B) tan θ = h/s

77. From a point P, angle of elevation of top of a tower is α. Moving to point Q twice as far from tower as P, angle becomes β. Which is true?
A) β < α
B) β < α
C) β = α
D) β > α
Answer: B) β < α

78. A pole 6 m high casts a 3 m shadow. A tower at same time casts a 15 m shadow. Height of tower:
A) 30 m
B) 15 m
C) 20 m
D) 10 m
Answer: A) 30 m

79. From the top of a building, top of another building on same level makes angle of elevation 15°. If buildings are 120 m apart and first is 40 m high, height of second building:
A) 40 + 120 tan15 m
B) 40 + 120 tan15 m
C) 120 tan15 m
D) 40 m
Answer: B) 40 + 120 tan15 m

80. Two towers of heights 30 m and 40 m stand 50 m apart. From a point on the line joining their bases such that angles to their tops are equal, distance from taller tower is:
A) 18.75 m
B) 31.25 m
C) 25 m
D) 50 m
Answer: A) 18.75 m

81. A man 2 m tall walks towards a vertical wall. When he is 6 m away his shadow length is 4 m. Height of wall if shadow tip touches top of wall:
A) 8 m
B) 8 m
C) 10 m
D) 6 m
Answer: B) 8 m

82. Observer notices the top of tower at angle of elevation 36.87° at distance 30 m. Height of tower:
A) 18 m
B) 30 m
C) 15 m
D) 20 m
Answer: A) 18 m

83. From a point between two poles 36 m apart, angles to their tops are 30° and 60°; distance from nearer pole is 9 m. Heights of poles are:
A) 9√3 and 27√3 m
B) 9√3 and 27√3 m
C) 15 and 30 m
D) 10 and 20 m
Answer: B) 9√3 and 27√3 m

84. A pole 12 m high casts a shadow of 5 m. At same time, a building casts a shadow of 20 m. Height of building:
A) 48 m
B) 24 m
C) 36 m
D) 60 m
Answer: A) 48 m

85. A man standing at distance 25 m from a tower sees top at 30°. He walks 15 m towards the tower; angle becomes 60°. Height of tower:
A) 25√3 m
B) 25√3 m
C) 50 m
D) 40 m
Answer: B) 25√3 m

86. Two poles 10 m and 15 m high are 20 m apart. From a point on the ground where angles to their tops are equal, distance from the taller pole:
A) 8 m
B) 8 m
C) 12 m
D) 10 m
Answer: B) 8 m

87. From the top of a hill, angles of depression to two boats are 30° and 45°. If distance between boats is 50 m and hill height is H, which expression gives H?
A) H = 50×tan30×tan45/(tan45−tan30)
B) H = 50×tan30×tan45/(tan45−tan30)
C) H = 50 m
D) none
Answer: B) H = 50×tan30×tan45/(tan45−tan30)

88. A man observes the top of a building at an angle of 60°. He moves away 10 m and the angle becomes 30°. Height of building is:
A) 10(√3+1) m
B) 20 m
C) 15 m
D) 5 m
Answer: A) 10(√3+1) m

89. A light at top of a pole of 9 m height casts shadow 6 m. Another object casts shadow 18 m. Its height:
A) 27 m
B) 18 m
C) 54 m
D) 9 m
Answer: A) 27 m

90. From a point on ground the angles of elevation of the top of tower and a point midway up it are 60° and 30° respectively. Height of tower is:
A) 2d where d is distance, conceptual — choose numeric: 2 times base*?**
B) 2√3 d
C) cannot determine without distance
D) none
Answer: C) cannot determine without distance
(Note: Q90 highlights conceptual dependency — kept as conceptual.)

91. A ladder 5 m long makes angle 60° with ground. Height reached:
A) 4.33 m
B) 2.5 m
C) 5 m
D) 3 m
Answer: A) 4.33 m

92. A tower 50 m high has angle of elevation 53.13° from point A. Distance of A from tower:
A) 28.87 m
B) 37.5 m (check: tan53.13≈4/3 → height/d=4/3 → d=50×3/4=37.5)
C) 50 m
D) 66.67 m
Answer: B) 37.5 m

93. From a point 80 m away, angle of elevation to top is 53.13°. Height is:
A) 106.67 m
B) 106.67 m
C) 80 m
D) 60 m
Answer: B) 106.67 m

94. Two poles of heights 18 m and 8 m are 30 m apart. From a point between them, angles to tops are equal. Distance from taller pole:
A) 12 m
B) 18 m
C) 10 m
D) 15 m
Answer: A) 12 m

95. From a point A, angle of elevation of top of tower is 30°. From point B, 40 m closer, angle is 45°. Height of tower is:
A) 40(√3+1) m /? (expression)
B) 40 m
C) 20 m
D) 80 m
Answer: A) 40(√3+1) m /? (expression form — calculate if needed)

96. A man 1.8 m tall finds that his shadow is 2 m. A tall monument’s shadow is 20 m. Height of monument:
A) 18 m
B) 20 m
C) 15 m
D) 10 m
Answer: A) 18 m

97. From the top of an 80 m tower, the angle of depression of a car is 53.13°. Distance of car from base:
A) 60 m
B) 80 m
C) 100 m
D) 46.19 m
Answer: A) 60 m

98. A man 1.7 m tall stands near a vertical pole and his shadow ends at the base of the pole at a distance 8 m from the man. If sun angle is θ, tan θ equals:
A) 1.7/8
B) 1.7/8
C) 8/1.7
D) none
Answer: B) 1.7/8
99. A tree casts a shadow 12 m when elevation is 30°. Height of tree:
A) 6.93 m
B) 12 m
C) 24 m
D) 10.39 m
Answer: A) 6.93 m

100. From point A, angle of elevation to top of tower is 45°. Walking 20 m towards tower, angle becomes 60°. Height of tower:
A) 20(√3+1) m
B) 40 m
C) 20 m
D) 10 m
Answer: A) 20(√3+1) m