MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 37

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedSome Applications of Trigonometry

Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections 'A' and 'B'. Tower is supported by wires from a point 'O' (as shown in figure).

Distance between the base of the tower and point 'O' is 6 m. From point 'O', the angle of elevation of the top of the section 'B' is $3 0^{\circ}$ and the angle of elevation of the top of section 'A' is $6 0^{\circ}$ .

Based on the above information, answer the following questions :

(i)
Find the length of the wire from the point 'O' to the top of section 'B'.
1 mark
(ii)
Find the length of the wire from the point 'O' to the top of section 'A'.
1 mark
(iii)(a)
Find the distance AB.
2 marks
OR
(iii)(b)
Find the area of $Δ$ OPB.
2 marks

Figure in the paper: A vertical tower AP with P at the base on the ground and A at the top. Point B lies on the tower between P and A (section boundary). A point O on the ground is 6 m horizontally from P. Wires join O to A (angle of elevation 60° at O) and O to B (angle of elevation 30° at O). PO = 6 m is marked along the ground. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Each wire is the hypotenuse of a right triangle whose base is $O P = 6$ m.

Hint 2

Use cosine to find the wires and tangent to find the heights $B P$ and $A P$ .

Hint 3

$A B = A P - B P$ , and the area of $△ O P B$ is $\frac{1}{2} \times O P \times B P$ .

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) In right $△ O P B$ (right angle at $P$ ), $O P = 6$ m and $∠ B O P = 3 0^{\circ}$ :
$cos 3 0^{\circ} = \frac{O P}{O B} \Rightarrow \frac{3}{2} = \frac{6}{O B}$
½ mark
(i) $O B = \frac{12}{3} = 43 m$
½ mark
(ii) In right $△ O P A$ , $∠ A O P = 6 0^{\circ}$ :
$cos 6 0^{\circ} = \frac{O P}{O A} \Rightarrow \frac{1}{2} = \frac{6}{O A}$
½ mark
(ii) $O A = 12 m$
½ mark
(iii)(a) $tan 3 0^{\circ} = \frac{B P}{O P} \Rightarrow \frac{1}{3} = \frac{B P}{6} \Rightarrow B P = \frac{6}{3} = 23 m$
1 mark
(iii)(a) $tan 6 0^{\circ} = \frac{A P}{O P} \Rightarrow 3 = \frac{A P}{6} \Rightarrow A P = 63 m$
½ mark
(iii)(a) $A B = A P - B P = 63 - 23 = 43 m$
½ mark
(iii)(b) $tan 3 0^{\circ} = \frac{B P}{6} \Rightarrow B P = 23 m$
1 mark
(iii)(b) $△ O P B$ is right-angled at $P$ , so
$ar (△ O P B) = \frac{1}{2} \times O P \times B P = \frac{1}{2} \times 6 \times 23 = 63 m^{2}$
1 mark

Answer: (i) $43$ m; (ii) 12 m; (iii)(a) $43$ m, (iii)(b) $63$ m²

Where the marks are

(i) Uses $cos 3 0^{\circ} = 6/ O B$ (½ mark)
(i) $O B = 43$ m (½ mark)
(ii) Uses $cos 6 0^{\circ} = 6/ O A$ (½ mark)
(ii) $O A = 12$ m (½ mark)
(iii)(a) $B P = 23$ m (1 mark)
(iii)(a) $A P = 63$ m (½ mark)
(iii)(a) $A B = 43$ m (½ mark)
(iii)(b) $B P = 23$ m (1 mark)
(iii)(b) Area $= 63$ m² (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 paper2026 board paper, set 30/1/1 (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 2026: question 37

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry