Question : A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retreats 36 m from the bank, he finds that the angle is 30°. The breadth of the river is:
Option 1: 15 metres
Option 2: 18 metres
Option 3: 16 metres
Option 4: 11 metres
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Correct Answer: 18 metres
Solution :
Let the breadth of the river be AC = $x$ metres
Clearly $\tan 30°=\frac{AB}{AD}=\frac{h}{x+36}$
⇒ $\tan 60°=\frac{AB}{AD}=\frac{h}{x}$
⇒ $\frac{\tan 60°}{\tan 30°}=\frac{\frac{h}{x}}{\frac{h}{x+36}}$
⇒ $\frac{\sqrt3}{\frac{1}{\sqrt3}}=\frac{x+36}{x}$
⇒ $3x=x+36$
⇒ $x=18$ m
Hence, the correct answer is 18 metres.
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