Question

The angle of elevation of the top of a hill at the foot of a tower is 60º and the angle of depression from the top of tower to the foot of hill is 30º. If tower is 50 metre high, find the height of the hill.​

Answer 1

Answer:

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) = H/BC

⇒ BC√3 = H

⇒ H = 50√3*√3 = 150 m.

or ,do by  this process