An aeroplane at an altitude of $\displaystyle 200$ metres observes the angles of depression of opposite points on the two banks of a river to be $\displaystyle 45$° and $\displaystyle 60$°. Find the width of the river. (Use $\displaystyle \sqrt{3}=1.732$ )

\[y=\frac{200}{\sqrt{3}}=\frac{200 \sqrt{3}}{3} \] ∴ Width of river \(\displaystyle =A B=x+y=200+\frac{200 \sqrt{3}}{3}\) \[\begin{aligned} & A B=200+\frac{200(1 \cdot 732)}{3} \\ & =200+\frac{346 \cdot 4}{3}=200+115 \cdot 46=315 \cdot 46 \mathrm{~m} \end{aligned} \] ∴ Width of river \(\displaystyle =315.46 \mathrm{~m}\)