Question

A bridge across a river makes an angle of $ {45}^{0}$ with the river bank. If the length of the bridge across the river is $ 150 m$, what is the width of the river ?

Answer 1

Let us assume this is a right angle triangle ABC:

In right triangle $ABC$, we have:
$$\begin{gathered} \sin \left({45}^0\right)=\frac{BC}{AC} \\ \frac{1}{\sqrt{2}}=\frac{BC}{150} \\ BC=\frac{150}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ BC=75\sqrt{2}m \end{gathered}$$
Therefore, the width of the river is $75\sqrt{2}m$.