Height and Distance

Total Questions: 45

31. Two ships are on the opposite side of a lighthouse such that all three of them are collinear. The angles of depression of the two ships from the top of the lighthouse are 30° and 60°. If the ships are 230√3 m apart, then find the height of the light house (in m). [SSC CGL Tier II (02/03/2023)]

Correct Answer: (c) 172.5
Solution:

32. From the top of an upright pole 24√3 feet high, the angle of elevation of the top of an upright tower was 60°. If the foot of the pole was 60 feet away from the foot of the tower, what tall (in feet) was the tower? [SSC CGL Tier II (06/03/2023)]

Correct Answer: (a) 84√3
Solution:

33. The angle of elevation of the top of a tower from the top of a building whose height is 680 m is 45° and the angle of elevation of the top of the same tower from the foot of the same building is 60°. What is the height (in m) of the tower? [ SSC CGL Tier II (07/03/2023)]

Correct Answer: (a) 340(3 + √3)
Solution:

34. An airplane goes 14 km due east and then 48 km due north. How far is it from its initial position? [SSC CGL 13/12/2022 (3rd Shift)]

Correct Answer: (c) 50 km
Solution:

35. A person 1.8 metre tall is 30√3 metres away from a tower. If the angle of elevation from his eye to the top of the tower is 30 degree, then what is the height (in m) of the tower? [SSC CGL Tier II (08/08/2022)]

Correct Answer: (d) 31.8
Solution:

36. The foot of a ladder 25 m long is 7 m from the base of the building. If the top of the ladder slips by 4 m, then by how much distance will the foot of the ladder slide? [SSC CHSL 24/05/2022 (Morning)]

Correct Answer: (d) 8 m
Solution:

37. The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°? [SSC CGL 11/04/2022 (Morning)]

Correct Answer: (c) 52/3
Solution:

38. A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m). [SSC CGL 12/04/2022 (Morning)]

Correct Answer: (c) 96
Solution:

39. The angle of elevation of the top of a tall building from the points M and N at the distances of 72m and 128m, respectively, from the base of the building and in the same straight line with it, are complementary. The height of the building (in m) is? [SSC CGL 12/04/2022 (Afternoon)]

Correct Answer: (b) 96
Solution:

40. Exactly midway between the foot of two towers P and Q, the angle of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is: [SSC CGL 18/04/2022 (Morning)]

Correct Answer: (a) 1 : √3
Solution: