A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.

Question

Philoid · Accepted Answer

Let CD be a hill . C be the top and D be the top.

Let AB be the height of the ship = 10 m

Angle of elevation of the top of hill when observed from point B, θ₁ = 60°

Angle of depression of the base of hill when observed from point B, θ₂ = 30°

Using all these condition, we make a diagram.

AB = CP

In △BCP

BP = 10 tan 30°

In △BPD

PD = 10 m

So distance of ship from hill = BP

Height of hill = CP + PD = 10 + 10 = 20 m