Question

An aeroplane is flying at a height of $300m$ above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are ${45}^o$ and ${60}^o$ respectively. Find width of the river. $[Use\sqrt{3}=1.732]$

Answer 1

Let $A$ be the aeroplane $BD$ is the length of the river

$\tan {45}^o=\frac{AC}{BC}$

$1=\frac{300}{BC}$

$BC=300m$

$\tan {60}^o=\frac{AC}{CD}$

$\sqrt{3}=\frac{300}{CD}$

$CD=\frac{300}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$=\frac{300\sqrt{3}}{3}=100\sqrt{3}=1.732\times 100=173.2$

width of river $=BC+CD=300+173.2=473.2m$