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Question

A man on the deck of a ship, 14m above the water level, observes that the angle of elevation of the top of a cliff is 60 and angle of depression of the base of the cliff is 30. Find the height of the cliff.

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Solution

Let BD be the height of the cliff.

Let A be the position of the ship and E be the point of observation so that AE=14m.

Draw EC parallel to AB such that AB=EC.

Given that ABE=30,DEC=60

In the right angled ABE,tan30=AEAB

AB=AEtan30

AB=143

Thus, EC=143

In the right angled DEC,tan60=CDEC

CD=ECtan60

CD=(143)3=42 m

Thus, the height of the cliff,

BCD=BC+CD

=14+42
=56 m.

1035303_622627_ans_0a62722f71304c74a235ce66a2695d0e.jpg

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