Question

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

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

Answer 1

The correct option is D $20m$

Let $R$ br the length of River

and $T$ be the length of tree

In $△ABC$

$\tan {60}^o=\frac{T}{R}\Rightarrow T=\sqrt{3}R.......\left(1\right)$

in $△ABD$

$\tan {30}^o=\frac{T}{R+40}\Rightarrow T=\frac{R+40}{\sqrt{3}}.....\left(2\right)$

From (1) and (2)

$\sqrt{3}R=\frac{R+40}{\sqrt{3}}\Rightarrow 3R=R+40\Rightarrow R=20$

Therefore, Answer is $20m$