Question

An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45 and 60. Find the width ofthe river

• A. 115.47 metres
• B. 200 metres
• C. 215.47 metres
• D. 315.47 metres

Answer 1

The correct option is D 315.47 metres

$\tan \theta =\frac{p}{b}\Rightarrow \tan {45}^{\circ }=\frac{y}{200}-\left(i\right)$

Similarity,

$\tan {30}^{\circ }=\frac{p}{b}=\frac{x}{200}-\left(ii\right)$

$1=\frac{y}{200}\Rightarrow y=200$

$\frac{1}{\sqrt{3}}=\frac{x}{200}\Rightarrow x=\frac{200}{\sqrt{3}}$

Suppose, $w=x+y$

$=200+\frac{200}{\sqrt{3}}$

$=200[1+\frac{1}{\sqrt{3}}]$