MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 23

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCompetency-basedSome Applications of Trigonometry

Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation $θ$ of the sun is such that $tan θ = \frac{6}{7}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Draw the pole, its shadow and the sun's ray as a right triangle.

Hint 2

The pole is opposite to $θ$ and the shadow is adjacent to it. Which ratio links these two sides?

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.

Let AB = 18 m be the pole and AP its shadow, with $∠ A P B = θ$ and $∠ A = 9 0^{\circ}$ . In right $△ P A B$ , $tan θ = \frac{A B}{A P} = \frac{18}{A P}$ .
1 mark
Substituting $tan θ = \frac{6}{7}$ : $\frac{6}{7} = \frac{18}{A P}$ .
½ mark
$A P = \frac{18 \times 7}{6} = 21$ m, so the shadow is 21 m long.
½ mark

Answer: Length of shadow = 21 m

Where the marks are

Sets up $tan θ = \frac{18}{A P}$ in the right triangle (1 mark)
Substitutes $\frac{6}{7}$ (½ mark)
Gets AP = 21 m (½ mark)

Revise the chapter

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

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 paper2023 board paper, set 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 23

Hints

Step-by-step solution

Revise the chapter

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