Question

A man sitting in an aeroplane observes that the angles of depression of two temples 2 km apart are 60°. If the plane is exactly above the middle point of the line joining the temples, calculate its height.

Answer 1

A and B represent the temples and P the aeroplane

\(\frac{PM}{AM}\) = tan 60° ⇒ \(\frac{PM}{1}\) = tan 60°

⇒ PM = 1 tan 60° = √3

Hence the plane is at a height of √3 km.