A man sitting at a height of 20 m on a tall tree on

Solution:

Let  be the width of river. And the angles of depression on either side of the river are 30° and 60° respectively. It is given that AC = 20 m. Let BC = x and CD = y. And , 

Here we have to find the width of river.

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle,

$\Rightarrow \quad \tan B=\frac{A C}{B C}$

$\Rightarrow \quad \tan 30^{\circ}=\frac{20}{x}$

$\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{20}{x}$

$\Rightarrow \quad x=20 \sqrt{3}$

Again in a triangle 

$\Rightarrow \quad \tan D=\frac{A C}{C D}$

$\Rightarrow \quad \tan 60^{\circ}=\frac{20}{y}$

$\Rightarrow \quad \sqrt{3}=\frac{20}{y}$

$\Rightarrow \quad y=\frac{20}{\sqrt{3}}$

$\Rightarrow \quad x+y=20 \sqrt{3}+\frac{20}{20 \sqrt{3}}$

$\Rightarrow \quad x+y=\frac{80}{\sqrt{3}}$

Hence width of river is $\frac{80}{\sqrt{3}} \mathrm{~m}$.