CBSE Class 10 Mathematics Basic 2023: question 32(B)

Hints

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Step-by-step solution

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1. Figure: building AB = 7 m (A on ground, B top), tower PQ with foot P and top Q, $AP=x$. Draw $BC\parallel AP$ meeting PQ at C, so $BC=x$, $CP=7$ m, $CQ=h$. $\angle QBC=60^{\circ }$ (elevation), $\angle CBP=45^{\circ }=\angle BPA$ (depression = alternate angle).

   1 mark

2. In right $△BAP$: $\tan 45^{\circ }=\frac{AB}{AP}=\frac{7}{x}\Rightarrow 1=\frac{7}{x}\Rightarrow x=7$ m

   1½ marks

3. In right $△BCQ$: $\tan 60^{\circ }=\frac{CQ}{BC}=\frac{h}{x}\Rightarrow h=\sqrt{3}x$

   1½ marks

4. $h=7\sqrt{3}$ m

   ½ mark

5. Height of tower $PQ=PC+CQ=7+7\sqrt{3}=7(1+\sqrt{3})$ m (≈ 19.12 m)

   ½ mark

Answer: Height of tower = 7(1 + √3) m (≈ 19.12 m)

Revise the chapter

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