#### Question

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

#### Solution

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 ∠ABC = 30°, ∠ADC = 60°

Here we have to find height of cliff.

So we use trigonometric ratios

In a triangle ABC

`=> tan B = (AC)/(BC)`

`=> tan 30^@ = 80/x`

`=> 1/sqrt3 = 80/x`

`=> x = 80sqrt3`

Again in a triangle ADC

`=> tan D = (AC)/(CD)`

`=> tan 60^@ = 80/y`

`=> sqrt3 = 80/y`

`=> y = 80/sqrt3`

`=> x + y = 80sqrt3 + 80/sqrt3`

`=> x + y = 320/sqrt3`

=> x + y = 184.8

Hence the height of cliff is 184.8 m