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

CBSE Class 10 Mathematics Standard 2023: question 24(a)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerCompetency-basedSome Applications of Trigonometry

The length of the shadow of a tower on the plane ground is $3$ times the height of the tower. Find the angle of elevation of the sun.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Draw a right triangle: tower vertical, shadow along the ground.

Hint 2

Which trigonometric ratio links the opposite side (height) and the adjacent side (shadow)?

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 $A B = h$ be the tower and $A C$ its shadow, so $A C = 3 h$ . Let $θ$ be the angle of elevation of the sun at C.
In right $△ B A C$ : $tan θ = \frac{A B}{A C} = \frac{h}{3 h}$
1 mark
$tan θ = \frac{1}{3}$
½ mark
$\Rightarrow θ = 3 0^{\circ}$
½ mark

Answer: Angle of elevation of the sun = $3 0^{\circ}$

Where the marks are

Writes $tan θ = \frac{h}{3 h}$ (1 mark)
Simplifies to $tan θ = \frac{1}{3}$ (½ mark)
Concludes $θ = 3 0^{\circ}$ (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 paper2023 board paper, set 30/2/1 (Standard): 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.

CBSE Class 10 Mathematics Standard 2023: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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