MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2025: question 36

Set in the CBSE Class 10 board exam of 2025, 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: Reena, a girl, flying a kite from the ground with a straight string making an inclination with the ground. Right: Ravi standing on a rooftop balcony of a 10 m high building, flying a kite high above the town, with the string making angle theta at the rooftop. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 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 of a right triangle; the vertical height is the side opposite the angle.

Hint 2

For Ravi, measure the height from the rooftop, not the ground. Subtract or add the 10 m building height.

Hint 3

Use $sin (angle) = \frac{opposite}{hypotenuse}$ with a hypotenuse of 120 m.

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) Reena's string is the hypotenuse $l$ , the kite height is 60 m and the inclination is $3 0^{\circ}$ :
$sin 3 0^{\circ} = \frac{60}{l} \Rightarrow \frac{1}{2} = \frac{60}{l} \Rightarrow l = 120$ m
1 mark
(ii) Ravi's kite is 60 m above the ground and the rooftop is 10 m high. So the height of the kite above the rooftop is $60 - 10 = 50$ m. The string length is also 120 m.
$sin θ = \frac{50}{120} = \frac{5}{12}$
1 mark
(iii)(a) With $θ = 6 0^{\circ}$ and string 120 m, let $x$ be the height of the kite above the rooftop:
$sin 6 0^{\circ} = \frac{x}{120} \Rightarrow x = 120 \times \frac{3}{2} = 603$ m
1 mark
(iii)(a) Height above the ground $= 603 + 10 = 60 (1.7) + 10$
½ mark
(iii)(a) $= 102 + 10 = 112$ m
½ mark
(iii)(b) With an inclination of $3 0^{\circ}$ and string 120 m, the height of the kite above the rooftop is $x$ :
$sin 3 0^{\circ} = \frac{x}{120} \Rightarrow x = 120 \times \frac{1}{2} = 60$ m
1 mark
(iii)(b) Height above the ground $= 60 + 10 = 70$ m
1 mark

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) Takes the height above the rooftop as 50 m and gets $sin θ = 5/12$ (1 mark)
(iii)(a) Gets $x = 603$ from $sin 6 0^{\circ} = x /120$ (1 mark)
(iii)(a) Adds the 10 m building height (½ mark)
(iii)(a) Final height 112 m (½ mark)
(iii)(b) Gets $x = 60$ m from $sin 3 0^{\circ} = x /120$ (1 mark)
(iii)(b) Height $= 60 + 10 = 70$ 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 paper2025 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 2025: question 36

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry