CBSE Class 10 Mathematics Standard 2024: question 33

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Step-by-step solution

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1. Figure: P is the point on the bridge, Q is the foot of the perpendicular from P on the line of the banks, PQ = 4 m. A and B are the banks on opposite sides of Q. Angles of depression from P are 30° to A and 60° to B, so $\angle PAQ=30^{\circ }$ and $\angle PBQ=60^{\circ }$ [alternate angles]. Let AQ = x, QB = y; width AB = x + y.

   1 mark

2. In right $△PQA$: $\tan 30^{\circ }=\frac{PQ}{AQ}\Rightarrow \frac{1}{\sqrt{3}}=\frac{4}{x}$

   1 mark

3. $x=4\sqrt{3}$ m

   ½ mark

4. In right $△PQB$: $\tan 60^{\circ }=\frac{PQ}{QB}\Rightarrow \sqrt{3}=\frac{4}{y}$

   1 mark

5. $y=\frac{4}{\sqrt{3}}$ m

   ½ mark

6. 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 ($\approx 9.24$ m)

   1 mark

Answer: Width of river $=\frac{16\sqrt{3}}{3}$ m (≈ 9.24 m)

Revise the chapter

• Chapter: Some Applications of Trigonometry (notes, formulas, where marks are lost and every past question)
• Topic: Angle of Depression