MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 22(A)

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section B, question 22(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(A) · 2 marks · Very short answerCompetency-basedSome Applications of Trigonometry

A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the length of his shadow after 3 seconds.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

First find how far the boy is from the lamp post after 3 seconds.

Hint 2

The lamp post and the boy are both vertical, so the two right triangles sharing the shadow tip are similar.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Figure: lamp post AB = 12 m with B on the ground; boy CD = 1.5 m standing at D; the line from the lamp top A through the boy's head C meets the ground at E, so DE = $x$ m is the shadow. B, D, E lie on the ground line.
½ mark
Distance walked in 3 s $= 2.5 \times 3 = 7.5$ m, so BD = 7.5 m and BE = $(7.5 + x)$ m.
½ mark
In $Δ A B E$ and $Δ C D E$ : $∠ B = ∠ D = 9 0^{\circ}$ and $∠ E$ is common, so $Δ A B E \sim Δ C D E$ (AA). Hence $\frac{C D}{A B} = \frac{D E}{B E}$ .
½ mark
$\frac{1.5}{12} = \frac{x}{7.5 + x} \Rightarrow 12 x = 11.25 + 1.5 x \Rightarrow 10.5 x = 11.25 \Rightarrow x = \frac{15}{14} \approx 1.07$ m.
Length of shadow ≈ 1.07 m.
½ mark

Answer: Shadow $= \frac{15}{14}$ m ≈ 1.07 m

Where the marks are

Correct labelled figure (½ mark)
Distance covered in 3 s = 7.5 m (½ mark)
Uses similarity $Δ A B E \sim Δ C D E$ to write $\frac{C D}{A B} = \frac{D E}{B E}$ (½ mark)
Solves to get shadow ≈ 1.07 m (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Some Applications of Trigonometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 22(A)

Hints

Step-by-step solution

Revise the chapter

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