Question

An aeroplane is flying at a height of 300 m above a river. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the width of the river [Use $\sqrt{3}$ = 1.7321

Answer 1

Let aeroplane is at A, 300 m high from the river. C and D are opposite banks of river.
In right $\Delta ABC$
$\frac{BC}{AB}=\text{cot}{60}^{\circ }$
$\Rightarrow \frac{x}{300}=\frac{1}{\sqrt{3}}\Rightarrow x=\frac{300}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$
= $100\sqrt{3}m$
= $100\times 1.732=173.2$ m
In right $\Delta ABD$,
$\Rightarrow \frac{BD}{AB}=cot{45}^{\circ }$
$\Rightarrow \frac{y}{300}=1\Rightarrow y=300m$
Width of river = x + y
=173.2+300
=473.2 m