Case Study – 1 An injured bird was found on the roof of a building. The building is 15 m high. A fireman was called to rescue the bird. The fireman used an adjustable ladder to reach the roof. He placed the ladder in such a way that the ladder makes an angle of 60° with the ground in order to reach the roof. Based on the above information, answer the following questions : (i) Find the length of the ladder used by the fireman to reach the roof. (ii) Find the distance of the point on the ground at which the ladder was fixed from the bottom of the building. (iii) (a) In order to avoid skidding, the fireman placed the ladder in such a way that the bottom of the ladder touches the base of the wall which is opposite to the building, making an angle of 30° with the ground. Draw a neat diagram to represent the above situation and hence find the width of the road between the building and the wall. (iii) (b) Find the length of the ladder used by the fireman in this case.

(i) 103 17.32 m; (ii) 53 8.66 m; (iii)(a) width = 153 25.98 m; (iii)(b) 30 m

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/1/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2026: question 36

Set in the CBSE Class 10 board exam of 2026, paper 430/1/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedSome Applications of Trigonometry

Case Study – 1

An injured bird was found on the roof of a building. The building is 15 m high. A fireman was called to rescue the bird. The fireman used an adjustable ladder to reach the roof. He placed the ladder in such a way that the ladder makes an angle of $6 0^{\circ}$ with the ground in order to reach the roof.

Based on the above information, answer the following questions :

(i)
Find the length of the ladder used by the fireman to reach the roof.
1 mark
(ii)
Find the distance of the point on the ground at which the ladder was fixed from the bottom of the building.
1 mark
(iii)
(a) In order to avoid skidding, the fireman placed the ladder in such a way that the bottom of the ladder touches the base of the wall which is opposite to the building, making an angle of $3 0^{\circ}$ with the ground. Draw a neat diagram to represent the above situation and hence find the width of the road between the building and the wall.
2 marks
OR
(iii)
(b) Find the length of the ladder used by the fireman in this case.
2 marks

Figure in the paper: Photo of a fireman on a ladder reaching a bird on a roof; schematic: a vertical building wall of height 15 m, a ladder leaning against it making 60° with the ground, with its foot on the ground away from the wall. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/1/1.

Hints

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

Hint 1

The building, the ground and the ladder form a right triangle in which the height is 15 m.

Hint 2

The ladder is the hypotenuse, so use sine to find it; use tangent for the distance along the ground.

Hint 3

In part (iii), the angle at the foot of the ladder becomes 30°. Repeat the same ratios with this angle.

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.

(i) Let the ladder have length $l$ . Then $sin 6 0^{\circ} = \frac{15}{l} \Rightarrow \frac{3}{2} = \frac{15}{l} \Rightarrow l = \frac{30}{3} = 103 \approx 17.32$ m.
1 mark
(ii) Let the distance be $d$ . Then $tan 6 0^{\circ} = \frac{15}{d} \Rightarrow 3 = \frac{15}{d} \Rightarrow d = \frac{15}{3} = 53 \approx 8.66$ m.
1 mark
(iii)(a) Diagram: draw a vertical line AB = 15 m for the building (B on the ground) and mark C, the base of the opposite wall, on the ground. Join AC as the ladder, with $∠ A C B = 3 0^{\circ}$ and $∠ A B C = 9 0^{\circ}$ . BC is the width of the road.
1 mark
(iii)(a) $tan 3 0^{\circ} = \frac{A B}{B C} \Rightarrow \frac{1}{3} = \frac{15}{B C} \Rightarrow B C = 153 \approx 25.98$ m.
1 mark
(iii)(b) In the same right triangle, $sin 3 0^{\circ} = \frac{A B}{A C} \Rightarrow \frac{1}{2} = \frac{15}{A C}$ .
1 mark
(iii)(b) Therefore $A C = 30$ m, so the ladder is 30 m long.
1 mark

Answer: (i) $103 \approx 17.32$ m; (ii) $53 \approx 8.66$ m; (iii)(a) width $= 153 \approx 25.98$ m; (iii)(b) 30 m

Where the marks are

(i) Uses $sin 6 0^{\circ}$ to get ladder length $103$ m (1 mark)
(ii) Uses $tan 6 0^{\circ}$ to get distance $53$ m (1 mark)
(iii)(a) Correct labelled diagram (1 mark)
(iii)(a) Uses $tan 3 0^{\circ}$ to get width $153$ m (1 mark)
(iii)(b) Uses $sin 3 0^{\circ} = \frac{15}{A C}$ (1 mark)
(iii)(b) Gets ladder length 30 m (1 mark)

Revise the chapter

Chapter: Some Applications of Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Heights and Distances: One Right Triangle

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 paper2026 board paper, set 430/1/1 (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.

CBSE Class 10 Mathematics Basic 2026: question 36

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry