Question

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) 200 m

(b) 500 m

(c) 30 m

(d) 400 m

Answer 1

Let be the surface of the lake and be the point of observation. So m.

The given situation can be represented as,

Here, is the position of the cloud and is the reflection in the lake. Then .

Let be the perpendicular from on . Then and .

Let , , then and

Here, we have to find the height of cloud.

So we use trigonometric ratios.

In ,

Again in,

Put

Now,

Hence the correct answer is .