Question

An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the width of the river. Write the answer correct to the nearest whole number. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

In $\Delta OMA$

$tan{45}^{\circ }=\frac{OM}{AM}$

$I=\frac{250}{x}$ $\{\because tan{45}^{\circ }=1\}$



$\Rightarrow x=250m$

In $\Delta OMB,tan{60}^{\circ }=\frac{250}{y}$

$\Rightarrow \sqrt{3}=\frac{250}{y}\Rightarrow y=\frac{250}{\sqrt{3}}=\frac{250}{1.73}$

$y=144.34$

$\therefore$ Width of river = x + y = 250 + 144.34

= 394.34 m