Quantitative Aptitude - Heights & Distances

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Question - 1

The angle of elevation of the sun, when the length of the shadow of a tree is \(\sqrt3\) times the height of the tree is :

  • A \(30°\)
  • B \(45°\)
  • C \(60°\)
  • D \(90°\)

Question - 2

From a point P on a level ground, the angle of elevation of the top of a tower is \(30°\). If the tower is 100 m high, the distance of point P from the foot of the tower is :

  • A 149 m
  • B 156 m
  • C 173 m
  • D 200 m

Question - 3

The angle of elevation of a ladder leaning against a wall is \(60°\) and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is :

  • A 2.3 m
  • B 4.6 m
  • C 7.8 m
  • D 9.2 m

Question - 4

An observer 1.6 m tall is \(20\sqrt3\) away from a tower. The angle of elevation from his eye to the top of the tower is \(30°\). The height of the tower is :

  • A 21.6 m
  • B 23.2 m
  • C 24.72 m
  • D None of these

Question - 5

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are \(30°\) and \(45°\) respectively. If the lighthouse is 100 m high, the distance between the two ships is :

  • A 173 m
  • B 200 m
  • C 273 m
  • D 300 m

Question - 6

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of \(30°\) with the man's eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes \(60°\). What is the distance between the base of the tower and the point P ?

  • A \(4\sqrt3\) units
  • B 8 units
  • C 12 units
  • D Data inadequate 
  • E None of these

Question - 7

The angle of elevation of the top of a tower from a certain point is \(30°\). If the observer moves 20 m towards the tower, the angle of elevation of the top of the tower increases by \(15°\). The height of the tower is :

  • A 17.3 m
  • B 21.9 m
  • C 27.3 m
  • D 30 m

Question - 8

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of \(45°\) with the man's eye when at a distance of 60 metres from the tower. After 5 seconds, the angle of depression becomes \(30°\). What is the approximate speed of the boat, assuming that it is running in still water ?

  • A 32 kmph
  • B 36 kmph
  • C 38 kmph
  • D 40 kmph
  • E 42 kmph

Question - 9

On the same side of a tower, two objects are located. Observed from the top of the tower, their angle of depression are \(45°\) and \(60°\). If the height of the tower is 150 m, the distance between the objects is :

  • A 63.5 m
  • B 76.9 m
  • C 86.7 m
  • D 90 m

Question - 10

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from \(30°\) to \(45°\), how soon after this will the car reach the observation tower ?

  • A 14 min. 35 sec
  • B 15 min. 49 sec.
  • C 16 min. 23 sec.
  • D 18 min. 5 sec.