Question

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

Answer 1

Step-by-step explanation:

Let AB be the tower and CD be the hill. Then, ∠ACB=30o,∠CAD=60o and AB=50 m.

Let CD=x m

In right △BAC, we have,

cot30o=ABAC

3=50AC

AC=503 m

In right △ACD, we have,

tan60o=ACCD

3=503x

x=50×3=150 m

Therefore, the height of the hill is 150 m.