Question

A man standing on the bank of the river observes that the angle subtended by a tree on the opposite bank is ${60}^0$. When he retires $36$ metres from the bank he finds the angle to be ${30}^0$. The breadth of the river is

• A. $12\sqrt{3}$m
• B. $18m$
• C. $12m$
• D. $27m$

Answer 1

The correct option is B $18m$

Let the breadth of the river be AC = 'x' metres
Clearly $\tan {30}^0=\frac{AB}{AD}=\frac{h}{x+36}$ and
$\tan {60}^0=\frac{AB}{AD}=\frac{h}{x}$
$\Rightarrow \frac{\tan {60}^0}{\tan {30}^0}=\frac{h}{x}÷\frac{h}{x+36}$
$\Rightarrow 3=\frac{x+36}{x}$
$\Rightarrow x=18m$