Question

The angle of elevation of the top of a hill from the foot of tower is 60 degree and the angle of elevation of the top of the tower from the foot of the hill is 30 degree. If the tower is 50m high, what is the height of the hill?

Answer 1

Let the height of the hill be x metres

Let the height of the hill be AB and that of the tower is CD

Then in triangle ABD

tanA = AB/BD

tan 60 = h / BD

√3 = h / BD

h = BD√3 m ------- eqn 1

Now, in triangle CDB

tan A = CD / BD

tan 30 = 50 / BD

1/√3 = 50/BD

BD = 50√3m

Now, from eqn 1

h = BD√3 m

h = 50√3 * √3

h = 150 m

Thus, the height of the hill is 150m.

Hope this helps :)