Question

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.

Answer 1

Let AB be the tower and CD be the hill

tan 60^∘ = `h/d`

`sqrt3 = h/d => h = sqrt3 d`   ...(1)

tan30^∘ `= 50/d`

`1/sqrt3 = 50/d => d = 50sqrt3   ...(2)`

`h = sqrt3 (50sqrt3) = 50xx3 = 150`

Height of hill = 150 m