MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2026: question 36

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, 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

Kite festival is a popular festival in India which takes place during Makar Sankranti. The festival is celebrated by people flying kites from their rooftops. Reena and Ravi are also flying kites to enjoy the festival. The height of Reena's kite is 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground, and the inclination of the string with the ground is $3 0^{\circ}$ . Ravi is flying a kite from a 10 m high building. His kite is also flying 60 m above the ground and the length of the string used by Ravi is same as that of Reena's. $θ$ is the angle of elevation of Ravi's kite from a point on the rooftop.

Based on the above information, answer the following questions :

(i)
Find the length of string used by Reena.
1 mark
(ii)
Find the value of $sin θ$ .
1 mark
(iii)
(a) If $θ$ changes to $6 0^{\circ}$ , without changing the length of the string, what will be the height of Ravi's kite above the ground ? (Use $3 = 1.7$ )
2 marks
OR
(iii)
(b) What would have been the height of Ravi's kite above the ground, if the string had an inclination of $3 0^{\circ}$ with the ground, assuming that the length of the string does not change ?
2 marks

Figure in the paper: Left: a girl (Reena) holding a string from the ground to a pink kite high in the air. Right: Ravi standing on a rooftop balcony of a 10 m high building, flying a kite high above the city, with the string going from his hand to the kite. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The string is the hypotenuse and the height is the side opposite the angle of elevation.

Hint 2

For Ravi, measure the height from the rooftop, not from the ground.

Hint 3

After finding the height above the roof, add the 10 m height of the building.

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 Reena's string length be $L$ . Then $sin 3 0^{\circ} = \frac{60}{L} \Rightarrow \frac{1}{2} = \frac{60}{L} \Rightarrow L = 120$ m.
1 mark
(ii) Ravi's kite is $60 - 10 = 50$ m above the rooftop, and his string is also 120 m long. So $sin θ = \frac{50}{120} = \frac{5}{12}$ .
1 mark
(iii)(a) With $θ = 6 0^{\circ}$ , height of the kite above the roof $= 120 sin 6 0^{\circ} = 120 \times \frac{3}{2} = 603 = 60 \times 1.7 = 102$ m.
1 mark
(iii)(a) Height above the ground $= 102 + 10 = 112$ m.
1 mark
(iii)(b) With an inclination of $3 0^{\circ}$ (measured at the rooftop, from a line parallel to the ground), height above the roof $= 120 sin 3 0^{\circ} = 60$ m. Height above the ground $= 60 + 10 = 70$ m.
2 marks

Answer: (i) 120 m; (ii) sin θ = 5/12; (iii)(a) 112 m; (iii)(b) 70 m

Where the marks are

(i) Uses $sin 3 0^{\circ} = 60/ L$ to get $L = 120$ m (1 mark)
(ii) Uses the height above the roof, 50 m, to get $sin θ = 5/12$ (1 mark)
(iii)(a) Finds $120 sin 6 0^{\circ} = 102$ m above the roof (1 mark)
(iii)(a) Adds the 10 m building to get 112 m (1 mark)
(iii)(b) Finds $120 sin 3 0^{\circ} = 60$ m and adds 10 m to get 70 m (2 marks)

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 paper2026 board paper, set 430/2/1 (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