A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the…

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^{\circ}$ and when he retires 40 meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is
  1. $20 \mathrm{~m}$
  2. $30 \mathrm{~m}$
  3. $40 \mathrm{~m}$
  4. $60 \mathrm{~m}$

Solution

$\tan 30^{\circ}=\frac{h}{40+b}$ $\Rightarrow \sqrt{3} h=40+b$ $\tan 60^{\circ}=h / b \Rightarrow h=\sqrt{3} b$ $\Rightarrow b=20 m$

Asked in: JEE Main 2004

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