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

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

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

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

The angle of elevation of the top of a tower from a point on the ground which is $30$ m away from the foot of the tower, is $3 0^{\circ}$ . Find the height of the tower.

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 the tower, the 30 m ground distance and the line of sight.

Hint 2

Use $tan 3 0^{\circ} = \frac{1}{3}$ and rationalise the answer.

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 $A B$ be the tower and C the point on the ground, with $A C = 30$ m and $∠ A C B = 3 0^{\circ}$ .
In right $△ B A C$ : $tan 3 0^{\circ} = \frac{A B}{A C} = \frac{A B}{30}$
1 mark
$A B = \frac{30}{3} = 103$
So the height of the tower is $103$ m (about 17.32 m).
1 mark

Answer: Height of tower = $103$ m

Where the marks are

Forms $tan 3 0^{\circ} = \frac{A B}{30}$ (1 mark)
Finds $A B = 103$ m (1 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(b)

Hints

Step-by-step solution

Revise the chapter

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