From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2024 · Standard
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585 Marks · March 2024 · Standard
From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are $30^{\circ}$ and $60^{\circ}$ respectively. If the bridge is at a height of $4 \text{ m}$ from the banks, find the width of the river.
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Correct Figure Let AB be the width of river In right $\triangle PAQ$, $\tan 30^{\circ} = \frac{1}{\sqrt{3}} = \frac{4}{x}$ $\Rightarrow 4\sqrt{3} = x$ In right $\triangle PBQ$, $\tan 60^{\circ} = \sqrt{3} = \frac{4}{y}$ $\Rightarrow y = \frac{4}{\sqrt{3}}$ Width of river = $x + y = 4\sqrt{3} + \frac{4}{\sqrt{3}} = \frac{16}{\sqrt{3}} \text{ m}$
