Question

A man standing on the deck of a ship, 18 m above the sea level, observes that the angle of elevation and depression respectively of the top and the bottom of a hill as 60° and 30°. Find the following:

Answer 1

Step-by-step explanation:

suppose man is standing on the Deck of a ship at point a such that AB = 18 m & let CE be the hill

Thus, AB = CD = 18 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/A

√3= h/x [tan 60° = √3]

h = √3x……..(1)

In ∆ ABC

tan 30° = AB /BC

[ tan30° = 1/√3]

1/√3 = 18/x

x= 18√3 m.. …………..(2)

h = √3x

h= √3× 18√3= 18 × 3= 54 m

h = 54 m

The height of the hill is CE= CD+ DE= 18 +54= 72 m