An aeroplane at an altitude of 3000 m observes the angles of depression of opposite points on the two banks of a river to be 45 and 60 respectively. Find the width of the river in metre.

Question

Question

This question was previously asked in

NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper

Answer 1

Given:

Altitude of aeroplane (h) = 3000 m

Angle of depression to first point = 45°

Angle of depression to second point = 60°

Formula used:

tan(θ) = h / x

Where θ is the angle of depression and x is the horizontal distance from the point directly below the aeroplane.

Calculations:

For the first point (angle 45°):

tan(45°) = 1

⇒ h / x₁ = 1

⇒ x₁ = h = 3000 m

For the second point (angle 60°):

tan(60°) = √3

⇒ h / x₂ = √3

⇒ x₂ = h / √3 = 3000 / √3 m

Width of the river = x₁ + x₂ = 3000 + 3000 / √3 = 4730 m (approx)

∴ The width of the river is approximately 4730 meters.