Question

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

• A. $40m$
• B. $60m$
• C. $20m$
• D. $30m$

Answer 1

Answer: (C)

$20m$

Let x be the breadth of the river
In $△$ ABC $\tan {60}^0=\frac{H}{x}$
$\sqrt{3}=\frac{H}{x}$
$H=\sqrt{3}x⟶1$
In $△$ DBE $\tan {30}^0=\frac{H}{BE}$
$\frac{1}{\sqrt{3}}=\frac{H}{x+40}$
$\frac{1}{\sqrt{3}}=\frac{\sqrt{3}x}{x+40}$ (From equation 1)
$3x=x+40$
$2x=40$
$x=20$
$\therefore$ Breadth of river is $20m$