Question

If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is

$\frac{2hsec\alpha }{\tan \beta -\tan \alpha }$

Answer 1

Let C′ be the image of cloud C. We have and.

Again let .and be the distance of cloud from point of observation.

We have to prove that

The corresponding figure is as follows

We use trigonometric ratios.

In

Again in

Now,

Again in

Hence distance of cloud from points of observation is