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Question

A tower of height 60 m stands on the top of a cliff. An observer in a boat finds that the elevation of the top of the tower is 60 and that of the top of the cliff is 30. Find the height of the cliff, and the distance of the boat from the foot of the cliff.

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Solution

If h is the height of cliff BC on which tower AB of height 60 m stands and D is the point at a distance x from the base of the cliff.

In BCD,
tan30=BCCD13=hxx=h3(i)

And, in BCD,
tan60=ACCD3=60+hx3x=60+h3×3h=60+h[By using(i)]3hh=602h=60h=30 m

By using (i),
x=3×30 m
=303 m

1080453_1006329_ans_7d16948ff95f476fac0d8897bed726ba.png

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