Discussion
The banks of a river are parallel. A swimmer starts from a point on one bank and swims in a straight line inclined to the bank at \( 45^{\circ} \), reaching the opposite bank after covering 20 m. What is the width of the river?
Answer: B
The swimmer's path is the hypotenuse. The width of the river is the perpendicular distance between the parallel banks, which is the side opposite the \( 45^{\circ} \) angle the path makes with the bank.
\[ \sin 45^{\circ} = \frac{\text{width}}{20} \]
\[ \text{width} = 20 \times \frac{1}{\sqrt{2}} = 10\sqrt{2} = 10 \times 1.414 = 14.14 \text{ m} \]
At \( 45^{\circ} \) the swimmer drifts exactly as far along the bank as the river is wide, so the 20 m swim splits into two equal legs of \( 10\sqrt{2} \) m.
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