MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 34

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerCompetency-basedSome Applications of Trigonometry

The angle of elevation of the top of a building from the foot of the tower is $3 0^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $6 0^{\circ}$ . If the tower is $60$ m high, find the height of the building and distance between the building and the tower. (Use $3 = 1.73$ )

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Draw the tower and the building as two vertical lines with the ground distance x between their feet.

Hint 2

Start with the tower: its height is known, so use the $6 0^{\circ}$ angle to find x.

Hint 3

Then use the $3 0^{\circ}$ angle from the foot of the tower with the same x to find the building's height.

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: let CD = 60 m be the tower (foot C) and AB = h m be the building (foot A), both vertical on level ground, with CA = x m. At A, the angle of elevation of D is $6 0^{\circ}$ ( $∠ D A C = 6 0^{\circ}$ ); at C, the angle of elevation of B is $3 0^{\circ}$ ( $∠ B C A = 3 0^{\circ}$ ).
1 mark
In right $△ D C A$ : $tan 6 0^{\circ} = \frac{D C}{C A} = \frac{60}{x}$
1 mark
$\Rightarrow 3 = \frac{60}{x} \Rightarrow x = \frac{60}{3} = 203 = 20 \times 1.73 = 34.6$ m
1 mark
In right $△ B A C$ : $tan 3 0^{\circ} = \frac{A B}{C A} = \frac{h}{x}$
1 mark
$\Rightarrow \frac{1}{3} = \frac{h}{20 3} \Rightarrow h = 20$ m
1 mark

Answer: Height of building = 20 m; distance between building and tower = $203$ m = 34.6 m

Where the marks are

Correct labelled figure (1 mark)
Uses $tan 6 0^{\circ} = \frac{60}{x}$ (1 mark)
Gets $x = 203 = 34.6$ m (1 mark)
Uses $tan 3 0^{\circ} = \frac{h}{x}$ (1 mark)
Gets $h = 20$ 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 paper2026 board paper, set 430/4/1 (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 34

Hints

Step-by-step solution

Revise the chapter

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