# 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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