Question

The angle of elevation of the summit of a hill from top and bottom of nearby tower are 30 degree 60 degree respectively. If the height of the tower is 100 m. Find the height of the hill.

Answer 1

Answer:

Explanation:

Let AB is the Tower of height = h = 50 m.

And,  let the Height of Hill CD = H m.

Distance between The root of the tower and hill = BC 

Now,

In ΔABC

∠C = 30°

    TAN(C) =  AB/BC

⇒ TAN(30) =  50/BC

⇒  1/√3 = 50 /BC

⇒ BC = 50√3 m.

Now,

In ΔBCD,

∠B = 60°

    Tan(B) = CD/BC

⇒ Tan(60) = Tan(60) = H/BC

⇒ BC√3 = H

⇒ H = 50√3*√3 = 150 m.