Question

A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the lighthouse.

Answer 1

Answer: 34.64 m

Explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

`\tan x=\frac{\text{Side opposite to }x}{\text{Side adjacent to }x}`

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

`\tan 37^(\circ)=(h)/(60)\\\\\Rightarrow\ 0.57735=(h)/(60)\\\\\Rightarrow\ h= 60*0.57735\approx34.64`

Hence, the lighthouse is 34.64 m tall.