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Question

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


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Solution

Let a man is standing on the deck of a ship at point a such that AB=10m

Let CE be the hill

Thus, AB=CD=10m

The top and bottom of a hill are E and C

Given:

The angle of depression of the base C of the hill observed from A is 30°

The angle of elevation of the top E of the hill observed from A is 60°

CAD=BCA=30° ( alternate angles)

Let AD=BC=xmand DE='h'm

In ADE , tan60°= Perpendicular / base

tan60°=DEAD

3=hx (tan60°=3)

h=3x………….equation 1

In ABC,tan30°=ABBC (tan30°=13)

13=10x

x=103m …………..equation 2

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

we have, h=3x=3×103=10×3=30m

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

Hence, the height of the hill is40m & the distance of the hill from the ship is 103m.


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