Question

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?

• A. $24$ m
• B. $20$ m
• C. $26$ m
• D. $15$ m

Answer 1

Answer: (B)

$20$ m

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 $20m$