From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are $30°$ and $60°$ respectively. If the bridge is at a height of 4 m from the banks, fi

Question

From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are $30°$ and $60°$ respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.

Accepted Answer

Step 1: Let $P$ be the point on the bridge, $A$ and $B$ be points on opposite banks. Height $= 4$ m.
Step 2: In right $	riangle PAQ$: $	an 30° = \frac{4}{x} \Rightarrow x = 4\sqrt{3}$ m
Step 3: In right $	riangle PBQ$: $	an 60° = \frac{4}{y} \Rightarrow y = \frac{4}{\sqrt{3}}$ m
Step 4: Width of river $= x + y = 4\sqrt{3} + \frac{4}{\sqrt{3}} = \frac{12 + 4}{\sqrt{3}} = \frac{16}{\sqrt{3}} = \frac{16\sqrt{3}}{3}$ m

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