Question

A man sitting at a height 20m on a tall tree on a small island in the middle of river observes two poles directly opposite each other on the two banks of river & in a line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is respectively. Find the width of river.

Answer 1

Let $BC$ be the width of river. And $\measuredangle$ of depression on either side of the river are ${30}^0$ and ${60}^0$ .

It is given that

$AC=20m$

Let $BC=x,CD=y,\angle ABC={30}^0,\angle ADC={60}^0$

In $△ABC$,

$\tan B=\frac{AC}{BC}$

$=\frac{20}{x}$

$=\frac{1}{\sqrt{3}}$

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

In $△ADC,\tan {60}^0=\frac{20}{y}$

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

$x+y=\frac{80}{\sqrt{3}}m=$ width of river