A bridge across a river makes an angle of 45∘ 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?

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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?

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71 \sqrt{13} m

75 \sqrt{2} m

72 \sqrt{5} m

70 \sqrt{3} m

answer is B.

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Detailed Solution

From the figure,
An angle made by bridge river =

45^{\circ}

The length of bridge AC= 150 m
Now in the 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 required width of the river =

75 \sqrt{2} m

.
Correct option is 2.

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