A Bridge Across A River Makes An Angle Of 45∘ With The River Bank. If The Length Of The Bridge Across The River Is 150 M, What Is The Width Of The River?

In right triangle ABC, we have

\(sin 45^{\circ} = \frac{BC}{AC}\) \(\Rightarrow \frac{1}{\sqrt{2}} = \frac{BC}{150}\) \(\Rightarrow BC = \frac{150}{\sqrt{2}}\) \(\Rightarrow BC = 75\sqrt{2}m\)

Therefore, the width of the river is \(75\sqrt{2}m metres.\)

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