Scholastic Aptitude Test - Mathematics - Hight and Distance

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Question - 1

The angle of elevation of the top of a tree from a point at a distance of 200 m from its base is 60°. The height of the tree is

  • A \(50\sqrt { 3 } m\)
  • B \(100\sqrt { 3 } m\)
  • C \(200\sqrt { 3 } m\)
  • D \(\frac { 200 }{ \sqrt { 3 } } m\)

Question - 2

An aeroplane flying horizontally 1km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°. The uniform speed of the aeroplane is

  • A 240kmph
  • B 240\(\sqrt { 2 } \) kmph
  • C 240 \(\sqrt { 3 } \) kmph
  • D none of these

Question - 3

The angle of elevation of a cloud at a height h above the level of water in a lake is \(\alpha\) and the angle of depression of its image in lake is \(\beta\) . Then, the height of the cloud above the surface of the lake is

  • A h cot \(\beta\)
  • B h(cot\(\alpha\) + cot \(\beta\))
  • C h cot \(\alpha\)
  • D \(h\left( \frac { cot\alpha +cot\beta }{ cot\alpha -cot\beta } \right) \)

Question - 4

A flagstaff of 5m high stands on a building of 25m height. An observer finds at a height of 30m, the flagstaff and the building subtend equal angles. The distance of the observer from the top of the flagstaff is

  • A 5m
  • B \(5\sqrt { 3 } m\)
  • C \(5\sqrt { \frac { 3 }{ 2 } } m\)
  • D none of these

Question - 5

If a flagstaff 6m high is placed on the top of a tower throws a shadow of 2\(\sqrt { 3 } \) m along the ground, then the angle that the seen makes with the ground is

  • A 60°
  • B 30°
  • C 90°
  • D none of these

Question - 6

A man on the top of a tower, standing on the sea-shore. finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° and 60°, How soon will the boat reach the sea-shore?

  • A 5 minute
  • B 10 minute
  • C \(\sqrt { 3 } \) minute
  • D None of these

Question - 7

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 take the car to reach the observation tower?

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

Question - 8

There are two temples, one on each bank of a river,just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other'temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.

  • A 31.14 m, 18 m
  • B 11.14 m, 18 m
  • C 21.14 m, 17 m
  • D none of these

Question - 9

A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36m from the bank, he finds the angle to be 30°. Find the breadth of the river.

  • A 15 m
  • B 16 m
  • C 17 m
  • D 18 m

Question - 10

The angular elevation of a tower from a point is 30°, at a point in a horizontal line to the foot of the tower and 100 metres nearest is 60°, find the height of the tower. Find the distance of the first point from the tower.

  • A \(50\sqrt { 3 } ,\quad 150m\)
  • B \(40\sqrt { 3 } ,\quad 140m\)
  • C \(30\sqrt { 3 } ,\quad 130m\)
  • D none of these
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