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A person standing on the bank of a river observes that the angle subtended by the tree on the opposite bank is $60^{o}$ and when he retires $40$ m from the bank and finds the angle of elevation to be $30^{o}$ . What is the breadth of the river?

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24

20

26

15

answer is B.

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Detailed Solution

It is given that as observed by a person standing on a bank of the river, the angle subtended by a tree on the opposite bank is 60° and from 40 m further away the angle of elevation becomes 30°.
Let

R

be the length of river and

T

be the length of the tree.
Question Image

△ ABC

\tan 60^{o} = \frac{T}{R}

⇒

T = \sqrt{3} R . . . . . . . (1)

△ ABD

\tan 30^{o} = \frac{T}{R + 40}

⇒

T = \frac{R + 40}{\sqrt{3}} . . . . . (2)

From (1) and (2)
⇒

\sqrt{3} R = \frac{R + 40}{\sqrt{3}}

⇒

3 R = R + 40

⇒

R = 20

m
Hence, the correct option is 2.

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