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A vertical pole of… (Class 10 Maths Basic 2025, Q22a)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, 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 vertical pole of height 10 m casts a shadow of 15 m on the ground and at the same time, a tower casts a shadow of 45 m on the ground. Find the height of the tower.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

The pole with its shadow and the tower with its shadow each form a right triangle. Why are these two triangles similar?

Hint 2

Set height ÷ shadow equal for the two objects and solve for the unknown height.

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.

  1. Let the pole be AB = 10 m with shadow BC = 15 m, and the tower be PQ = m with shadow QR = 45 m. Both stand vertically, so . The sun's rays make the same angle with the ground at the same time, so . Hence [AA similarity].

    ½ mark

  2. Corresponding sides are proportional:

    Height of the tower = 30 m.

    1½ marks

Answer: Height of the tower = 30 m

Where the marks are

  • Establishes that the pole-shadow triangle and the tower-shadow triangle are similar (½ mark)
  • Writes the proportion and gets the height as 30 m (1½ marks)

Revise the chapter

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 430/3/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.