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.
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