Question

A man is standing on the deck of a ship, which is 40 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. ( √3 =1. 732)​

Answer 1

Let a man is standing on the Deck of a ship at point a such that AB = 10 m & let CE be the hill

Thus, AB = CD = 10 m

The top and bottom of a hill is E and C.

Given, the angle of depression of the base C of the hill observed from A is 30° and angle of elevation of the top of the hill observed from A is 60 °

Then ∠EAD= 60° &

∠CAE= ∠BCA= 30°. (Alternate ANGLES)

Let AD = BC = x m & DE= h m

In ∆ ADE

tan 60° = Perpendicular / base = DE/AD

√3= h/x [tan 60° = √3]

h = √3x……..(1)

In ∆ ABC

tan 30° = AB /BC

[ tan30° = 1/√3]

1/√3 = 10/x

x= 10√3 m.. …………..(2)

Substitute the value of x from equation (2) in equation (1), we have

h = √3x

h= √3× 10√3= 10 × 3= 30 m

h = 30 m

The height of the hill is CE= CD+ DE= 10 +30= 40 m

Hence, the height of the hill is 40 m & the Distance of the hill from the ship is 10√3 m.

(Changed the values so you can practice it yourself)