CBSE Class 10 Mathematics Standard 2023: question 32(A)

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Step-by-step solution

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1. Figure: Let AB be the tower, with $AB=75$ m, A its foot and B its top. P and Q are the two cars on the highway, on the same side of the tower, with P nearer to A.

   Draw the horizontal line BX through B. The angles of depression are $\angle XBQ=30^{\circ }$ and $\angle XBP=60^{\circ }$.

   As BX ∥ AQ (alternate angles), $\angle BQA=30^{\circ }$ and $\angle BPA=60^{\circ }$.

   1 mark

2. In right $△BAP$:

   $\tan 60^{\circ }=\frac{AB}{AP}$, so $\sqrt{3}=\frac{75}{AP}$

   $AP=\frac{75}{\sqrt{3}}=25\sqrt{3}$ m

   1½ marks

3. In right $△BAQ$:

   $\tan 30^{\circ }=\frac{AB}{AQ}$, so $\frac{1}{\sqrt{3}}=\frac{75}{AQ}$

   $AQ=75\sqrt{3}$ m

   1½ marks

4. Distance between the cars:

   $PQ=AQ-AP=75\sqrt{3}-25\sqrt{3}=50\sqrt{3}$ m

   ½ mark

5. $PQ=50\times 1.73=86.5$ m

   ½ mark

Answer: 86.5 m

Revise the chapter

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