MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 34

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, 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 30 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 2025 board paper, set 430/5/1.

Hints

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

Hint 1

Draw two vertical lines (tower and building) on a common ground line; mark the angles from each foot to the other top.

Hint 2

Use $tan 6 0^{\circ}$ with the 30 m tower to find the distance first, then $tan 3 0^{\circ}$ for 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 = 30 m be the tower (foot C) and AB = $h$ m the building (foot A), with CA = $x$ m along the ground. Angle of elevation of D from A is $6 0^{\circ}$ ; angle of elevation of B from C is $3 0^{\circ}$ . $∠ D C A = ∠ B A C = 9 0^{\circ}$ .
1 mark
In right △ACD: $tan 6 0^{\circ} = \frac{C D}{C A} \Rightarrow 3 = \frac{30}{x} \Rightarrow x = \frac{30}{3} = 103$ …(i)
1½ marks
In right △CAB: $tan 3 0^{\circ} = \frac{A B}{C A} \Rightarrow \frac{1}{3} = \frac{h}{x} \Rightarrow x = h 3$ …(ii)
1½ marks
From (i) and (ii): $h 3 = 103 \Rightarrow h = 10$ m, and $x = 10 \times 1.73 = 17.3$ m.
Height of building = 10 m; distance between building and tower = 17.3 m.
1 mark

Answer: Height of building = 10 m; distance = 17.3 m

Where the marks are

Correct labelled figure (1 mark)
Uses $tan 6 0^{\circ}$ to get $x = 103$ (1½ marks)
Uses $tan 3 0^{\circ}$ to get $x = h 3$ (1½ marks)
Finds $h = 10$ m and $x = 17.3$ 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 430/5/1 (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 2025: question 34

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry