From an aeroplane vertically above a straight horizontal road

From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is

  1. (tan α + tan β) / (tan α tan β)
  2. (tan α tan β) / (tan α + tan β)
  3. (cot α cot β) / (cot α + cot β)
  4. (cot α + cot β) / (cot α cot β)

Answer

Let the height of the aeroplane be h. Because the stones are consecutive kilometer stones,

x + y = 1

From the right triangles,

tan α = h/x

tan β = h/y

h/tan α + h/tan β = 1

On solving further,

h = (tan α tan β) / (tan α + tan β)

The correct option is B.