Question

A bridge across a river makes an angle of 45${}^{\circ }$ with the river bank as shown in the figure. If the length of the bridge across the river is 150 m, what is the width of the river?

Answer 1

In right triangle ABC, we have
$sin{45}^{\circ }=\frac{BC}{AC}$
$\Rightarrow \frac{1}{\sqrt{2}}=\frac{BC}{150}$
$\Rightarrow BC=\frac{150}{\sqrt{2}}$
$\Rightarrow BC=75\sqrt{2}m$
Hence, the width of the river is $75\sqrt{2}m$ metres.