CBSE Class 10 Mathematics Basic sample paper 2026-27: question 35(A)

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Step-by-step solution

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1. Figure: Let A be the drone and B the accident site directly below it, with AB = $h$ m. D is the first position of the ambulance (angle of depression 30°, so $\angle ADB=30^{\circ }$). C is its position 12 minutes later (angle of depression 60°, so $\angle ACB=60^{\circ }$). D, C and B lie on a straight line, with $\angle ABC=90^{\circ }$.

   1 mark

2. Let the speed of the ambulance be $x$ m/min, so $CD=12x$ m.

   In right $△ABC$: $\tan 60^{\circ }=\frac{AB}{BC}\Rightarrow \sqrt{3}=\frac{h}{BC}\Rightarrow BC=\frac{h}{\sqrt{3}}$

   1 mark

3. In right $△ABD$: $\tan 30^{\circ }=\frac{AB}{BD}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{BD}\Rightarrow BD=h\sqrt{3}$

   1 mark

4. $BD=BC+CD\Rightarrow h\sqrt{3}=\frac{h}{\sqrt{3}}+12x\Rightarrow \frac{2h}{\sqrt{3}}=12x\Rightarrow h=6\sqrt{3}x$

   So $BC=\frac{6\sqrt{3}x}{\sqrt{3}}=6x$

   1 mark

5. Time from C to B $=\frac{6x}{x}=6$ minutes

   ½ mark

6. Total time taken $=12+6=18$ minutes

   ½ mark

Answer: 18 minutes

Revise the chapter

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