The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 meters, find the height of the chimney. Also, find the length of the wire tied from the top of the chimney to the top of tower.

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 34(A)

From the official CBSE sample question paper for 2025-26, section D, question 34(A), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(A) · 5 marks · Long answerSome Applications of Trigonometry

The angle of elevation of the top of a chimney from the foot of a tower is $6 0^{\circ}$ and the angle of depression of the foot of the chimney from the top of the tower is $3 0^{\circ}$ . If the height of the tower is 40 meters, find the height of the chimney. Also, find the length of the wire tied from the top of the chimney to the top of tower.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Draw the chimney and tower as two vertical lines on the same horizontal ground; the angle of depression from the top of the tower equals the angle of elevation at the foot of the chimney.

Hint 2

Use the tower (40 m) with $tan 3 0^{\circ}$ to get the distance between them, then $tan 6 0^{\circ}$ for the chimney.

Hint 3

For the wire, draw a horizontal line from the top of the tower to the chimney and use Pythagoras theorem.

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 AB be the chimney (B its foot) and CD the tower (C its foot), CD = 40 m, BC horizontal. $∠ A C B = 6 0^{\circ}$ (elevation of A from C) and $∠ D B C = 3 0^{\circ}$ (equal to the angle of depression of B from D, alternate angles). Draw DE ⟂ AB, so EBCD is a rectangle: EB = 40 m, ED = BC.
1 mark
In right $△ D C B$ : $tan 3 0^{\circ} = \frac{C D}{B C} \Rightarrow \frac{1}{3} = \frac{40}{B C} \Rightarrow B C = 403$ m. In right $△ A B C$ : $tan 6 0^{\circ} = \frac{A B}{B C} \Rightarrow 3 = \frac{A B}{40 3} \Rightarrow A B = 120$ m. Height of chimney = 120 m.
1½ marks
AE $= A B - E B = 120 - 40 = 80$ m and ED $= B C = 403$ m. In right $△ A E D$ : $A D = A E^{2} + E D^{2} = 6400 + 4800 = 11200 = 407$ m.
1½ marks
Hence the chimney is 120 m high and the wire from the top of the chimney to the top of the tower is $407$ m (≈ 105.83 m) long.
1 mark

Answer: Height of chimney = 120 m; length of wire = $407$ m (≈ 105.83 m)

Where the marks are

Correct labelled figure (1 mark)
Finds BC = $403$ m and AB = 120 m (1½ marks)
Finds AE = 80 m, ED = $403$ m and AD = $407$ m by Pythagoras (1½ marks)
Correct final statements (1 mark)

Revise the chapter

Chapter: Some Applications of Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Angle of Depression

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 paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 34(A)

Hints

Step-by-step solution

Revise the chapter

More questions from Some Applications of Trigonometry