Question

Two men on either side of the cliff 80 m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

Answer 1

Let AB and AD be the two men either side of cliff and height of cliff is 80 m.

And makes an angle of elevation, 30° and 60° respectively of the top of the cliff

We have given that AC = 80 m. Let BC = x and CD = y. And ,

Here we have to find height of cliff.

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle,

Again in a triangle

Hence the height of cliff is m.