Question

A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.

Answer 1

Distance between the ship and hill is 8√3 units and height of the hill is 32 units.

Step-by-step explanation:

AB = 8, BC = x, AD = BC, AB = DC, DE = h

∠ACB = 30° and ∠DAE = 60°

In ∆ABC, tan 30° = 8/x

 1/√3 = 8/x

Therefore x = 8√3 --------(1)

In ∆DAE, tan 60° = h/x

 √3 = h/x

 h = x√3-----------(2)

Substituting x in 2, we get: h = 8√3 * √3 = 24

Therefore H = h + 8 = 24 + 8 = 32

Distance between the ship and hill is 8√3 units and height of the hill is 32 units.