From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30°$ and $45°$ respectively. If the bridge is at a height of $3$ m from the banks, th

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From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30°$ and $45°$ respectively. If the bridge is at a height of $3$ m from the banks, then find the width of the river.

Accepted Answer

Step 1: Let $P$ be the point on bridge, $PD = 3$ m (height). $\frac{PD}{AD} = 	an 30° \Rightarrow AD = 3\sqrt{3}$ m.
Step 2: $\frac{PD}{BD} = 	an 45° = 1 \Rightarrow BD = 3$ m.
Step 3: Width $AB = AD + BD = 3\sqrt{3} + 3 = 3(\sqrt{3} + 1)$ m

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