CBSE Class 10 Mathematics Standard sample paper 2026-27: question 35(B)

Hints

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Step-by-step solution

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1. Figure (in words):

   • AB = $h$ is the lighthouse, with B at its foot.
   • C and D are the ships, on the same line through B, with D beyond C and CD = 200 m.
   • The angles of depression from A are 45° (to C) and 30° (to D).
   • Hence $\angle ACB=45^{\circ }$ and $\angle ADB=30^{\circ }$ [alternate angles].
   1 mark

2. In right $△ABC$: $\frac{h}{BC}=\tan 45^{\circ }=1$

   1 mark

3. $\Rightarrow BC=h$ ...(i)

   ½ mark

4. In right $△ABD$: $\frac{h}{BC+CD}=\tan 30^{\circ }\Rightarrow \frac{h}{h+200}=\frac{1}{\sqrt{3}}$

   1 mark

5. $\sqrt{3}h=h+200$

   $\Rightarrow h=\frac{200}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

   ½ mark

6. $h=\frac{200(\sqrt{3}+1)}{2}=100(\sqrt{3}+1)$ m $\approx 273.2$ m

   So the height of the lighthouse is $100(\sqrt{3}+1)$ m.

   1 mark

Answer: $100(\sqrt{3}+1)$ m (≈ 273.2 m)

Revise the chapter

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