If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake, is

A is the position of the cloud , B is the point 200 m above the lake and F is the reflection in the lake.

Here AE = EF

EF = (m + 200) m

In ΔABC

BC = m cot 30° ……………….1

In Δ BCF

CF = 200 + m +200

= (400 + m) meters

BC = (400 + m) cot 60° ………………….2

From 1 and 2

m cot 30° = (400 + m) cot 60°

m =

3 m = (400 + m)

m = 200 m

height above the cloud above the lake is (200 + 200)m = 400 m