An aeroplane flying at a height of 300 m above the ground passes

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

  1. 100√3 m
  2. 100/√3 m
  3. 50√3 m
  4. 150(√3 + 1) m

Answer

Let the ground distance between the point and the planes be x. The distance will be same for both the planes as they are vertical. The planes are at C and D.

AB = x

Let the height of lower plane be h.

BD = h

Given, BC = 300

tan 60° = 300/x

tan 45° = h/x

h = x = 300/tan 60°

h = 300/√3 = 100√3

The correct option is A.