The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places: Situation – I: The angle of elevation of the top of Statue from Place A which is 80√(3) m away from the base of the Statue is found to be 60°. Situation – II: The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be 30° and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions: (i) Represent the Situation – I with the help of a diagram. (ii) Represent the Situation – II with the help of a diagram. (iii) (a) Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation – I. (iii) (b) Find the horizontal distance of point B (Situation – II) from the Statue and the value of α, where α is the angle of elevation of top of base of the Statue from point B.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 38

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedSome Applications of Trigonometry

The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places:

Situation – I: The angle of elevation of the top of Statue from Place A which is $803$ m away from the base of the Statue is found to be $6 0^{\circ}$ .

Situation – II: The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $3 0^{\circ}$ and entire height of the Statue including the base is found to be 240 m.

Based on given information, answer the following questions:

(i)
Represent the Situation – I with the help of a diagram.
1 mark
(ii)
Represent the Situation – II with the help of a diagram.
1 mark
(iii)
(a) Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation – I.
2 marks
OR
(iii)
(b) Find the horizontal distance of point B (Situation – II) from the Statue and the value of $tan α$ , where $α$ is the angle of elevation of top of base of the Statue from point B.
2 marks

Figure in the paper: A figure of the Statue of Unity standing on a tall base, with two observers: Place A on the ground at the left and Place B standing on a raised platform of 40 m on the right. Both observers look through telescopes towards the top of the statue. The base of the statue is a stepped pedestal. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

In Situation I the statue with its base is the side opposite the 60° angle, and the 80√3 m distance is the adjacent side.

Hint 2

In Situation II draw a horizontal line from B to the statue. The part of the statue above this line is 240 − 40 m.

Hint 3

The top of the base is 58 m above the ground, so it is only 58 − 40 m above B's horizontal line.

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) Diagram: a vertical line CQ represents the statue with its base, with C on the ground and Q the top. Point A is on the ground with $A C = 803$ m. Join AQ and mark $∠ Q A C = 6 0^{\circ}$ , with a right angle at C. Mark P on CQ with $C P = 58$ m (the base).
1 mark
(ii) Diagram: a vertical line CQ with $C Q = 240$ m. A vertical platform EB stands with $B E = 40$ m and E on the ground. Draw horizontal BR to meet CQ at R, so $R C = 40$ m and $∠ QR B = 9 0^{\circ}$ . Join BQ and mark $∠ QB R = 3 0^{\circ}$ .
1 mark
(iii)(a) In right $△ A C Q$ : $\frac{QC}{A C} = tan 6 0^{\circ} = 3$ , so $QC = 803 \times 3 = 240$ m. Height including the base = 240 m.
1 mark
Height excluding the base $= 240 - 58 = 182$ m.
1 mark
(iii)(b) $QR = QC - R C = 240 - 40 = 200$ m.
½ mark
In right $△ QR B$ : $\frac{QR}{R B} = tan 3 0^{\circ} = \frac{1}{3}$ , so $R B = 2003$ m ( $\approx 346.4$ m). This is the horizontal distance of B from the statue.
½ mark
Diagram: P is the top of the base on CQ, so $P C = 58$ m and $P R = 58 - 40 = 18$ m. Right $△ P R B$ has the right angle at R and $∠ P B R = α$ .
½ mark
$tan α = \frac{P R}{R B} = \frac{18}{200 3} = \frac{3 3}{100}$ .
½ mark

Answer: (i), (ii) diagrams as described; (iii)(a) 240 m including base, 182 m excluding base; (iii)(b) horizontal distance 200√3 m, tan α = 3√3/100

Where the marks are

(i) Correct labelled diagram for Situation I (1 mark)
(ii) Correct labelled diagram for Situation II (1 mark)
(iii)(a) Uses $tan 6 0^{\circ}$ to get height including base 240 m (1 mark)
(iii)(a) Height excluding base 182 m (1 mark)
(iii)(b) $QR = 200$ m (½ mark)
(iii)(b) $R B = 2003$ m (½ mark)
(iii)(b) Figure of $△ P R B$ with $P R = 18$ m (½ mark)
(iii)(b) $tan α = \frac{3 3}{100}$ (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 paper2025 board paper, set 30/6/1 (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 2025: question 38

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry