Question

A man standing on the deck of the ship which is 10 metre above the sea level, observes the angle of elevation of the top of a cliff is 30 degree and angle of depression of the base of the cliff was found to be 60 degree. Find the height of the cliff and also the distance of cliff from the ship.

Answer 1

x=10√3
h=x√3
h=30m
Total height (till topmost point)=10+h
=40m
height of desk is 40 m and distance of desk from top point is 10√3m

Answer 2

The point of observation is at C


The height of the deck is 10 m
Thus, CD= EB = 10 m

The top and bottom of a hill is A & B

Let DB = CE = x m


In ∆ BDC

tan 30° = CD/DB = Perpendicular /Base

tan 30° = 10/x

1/√3= 10/x

x= 10√3

x= 10 × 1.732 = 17.32m

[ √3 = 1.732]

In ∆ AEC

tan 60° = AE/CE

√3= AE/10√3

AE = 10√3 × √3= 10 × 3= 30m

AE = 30 m

Height of the hill(AB) = AE + EB = 30+10= 40m

Height of the hill(AB) = 40 m

Distance of the hill from the ship (DB) = 17.32 m

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Hope this will help you....