Olympiad – Class X – Mathematics - Some Applications of Trignometry

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Question - 1

From a distance of 100 m from the foot of a building, the angle of elevation of its top is 30°. What is the height of the building?

  • A 57.7 m
  • B \(100\sqrt { 3 } m\)
  • C 5.77 m
  • D \(\frac { 100 }{ 3 } m\)

Question - 2

The angles of elevation of the top from two points on either side of a tree are 30° and 60°. What is the height of the tree if the two points are 52 m apart?

  • A 39m
  • B 22.5m
  • C 65m
  • D 225m

Question - 3

The angle of depression of a car from the top of a 20 m high tower is 60°. At what distance from the foot of the tower is the car?

  • A 16m
  • B 8m
  • C 22m
  • D 12m

Question - 4

The height of a kite from the ground is 100  lf the angle of elevation from a point on the ground is 45°, what is the length of the string of the kite?

  • A 100 \(\sqrt { 3 } \) m
  • B 100 \(\sqrt { 2 } \) m
  • C 100\(\sqrt { 6 } \) m
  • D 100m

Question - 5

A 24 m tall tree was cut to a height from the ground. The top of the tree touching the ground makes an angle 30° with the ground. At what height from the ground was the tree cut?

  • A 4m
  • B 8m
  • C 10m
  • D 6m

Question - 6

person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is 30°. He moves 40 m towards the bank and finds the angle of elevation to be 60°. What is the width of the river?

  • A 24m
  • B 20m
  • C 26m
  • D 15m

Question - 7

The angles of elevation of the sun changes from 45° to 30°.Then the shadow of a tower on the ground increases by 10 m. What is the height of the tower?

  • A 13.65m
  • B 13.56m
  • C 15.63m
  • D 15.36m

Question - 8

From an aeroplane at an altitude of 900 m, two cars moving towards it in the same direction are found to be 60° and 45°. What is the distance between the cars?

  • A 415m
  • B 315.4m
  • C 380.4m
  • D 305m

Question - 9

From a tower of 200 m, the angles of depression of two buildings in opposite sides of the tower are found to be 60° and 45°. What is the distance between the buildings?

  • A 415m
  • B 315.4
  • C 200m
  • D 305m

Question - 10

The angles of elevation of the top of a building from the ground floor and first floor of another building are 60° and 45° respectively. If the first floor is 40 m above the ground floor, what is the height of the building?

  • A 54.64 m
  • B 94.64m
  • C 40m
  • D 109.3
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