MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 33

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section D, question 33, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 5 marks · Long answerCompetency-basedSome Applications of Trigonometry

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $6 0^{\circ}$ and $3 0^{\circ}$ respectively. Find the height of the poles and the distance of the point from the poles.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Draw both poles with the observation point between them; let its distance from one pole be x, so it is (80 − x) from the other.

Hint 2

Write a tan equation in each right triangle and eliminate h.

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.

Figure: poles AB and CD, each of height $h$ m, at the two ends of road AC = 80 m, with right angles at A and C. O is the point on AC with AO = $x$ m, OC = $(80 - x)$ m; $∠ A O B = 6 0^{\circ}$ , $∠ C O D = 3 0^{\circ}$ .
1 mark
In right $△ D C O$ : $tan 3 0^{\circ} = \frac{C D}{C O} = \frac{h}{80 - x}$
1 mark
$\Rightarrow \frac{1}{3} = \frac{h}{80 - x} \Rightarrow 80 - x = h 3$ …(i)
½ mark
In right $△ B A O$ : $tan 6 0^{\circ} = \frac{h}{x} \Rightarrow h = x 3$ …(ii)
1 mark
Substituting (ii) in (i): $80 - x = 3 x \Rightarrow x = 20$ , so AO = 20 m and $h = 203$ m ( $\approx 34.64$ m).
1 mark
CO = $80 - 20 = 60$ m. Height of each pole = $203$ m; the point is 20 m from one pole and 60 m from the other.
½ mark

Answer: Height = $203$ m; distances 20 m and 60 m from the poles

Where the marks are

Correct labelled figure (1 mark)
$tan 3 0^{\circ} = \frac{h}{80 - x}$ (1 mark)
Simplifies to $80 - x = h 3$ (½ mark)
$tan 6 0^{\circ} = \frac{h}{x}$ giving $h = x 3$ (1 mark)
x = 20 m and $h = 203$ m (½ + ½ mark)
Other distance 60 m (½ 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 430/5/1 (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 33

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry