MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 34

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, 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

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $4 5^{\circ}$ and $6 0^{\circ}$ respectively. Find the height of the tower.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Draw the building and the tower as one vertical line. Mark the height of the building as 20 m and the height of the tower as h.

Hint 2

Use tan in both right triangles. They share the same horizontal distance x.

Hint 3

The 45° angle gives x directly. Then use $tan 6 0^{\circ} = (20 + h) / x$ .

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 $P$ be the point on the ground and $A$ the foot of the building. Let $A B = 20$ m be the building and $B C = h$ m the tower on top of it. Let $P A = x$ m. Then $∠ B P A = 4 5^{\circ}$ , $∠ C P A = 6 0^{\circ}$ and $∠ P A C = 9 0^{\circ}$ .
1 mark
In right $△ B P A$ : $tan 4 5^{\circ} = \frac{A B}{P A}$ , so $1 = \frac{20}{x}$ .
1 mark
Therefore $x = 20$ m ...(i)
½ mark
In right $△ C P A$ : $tan 6 0^{\circ} = \frac{A C}{P A}$ , so $3 = \frac{h + 20}{x}$ .
1 mark
Therefore $h + 20 = x 3$ ...(ii)
½ mark
Substitute (i) in (ii): $h + 20 = 203$ , so $h = 20 (3 - 1)$ m $\approx 14.64$ m.
Hence the height of the tower is $20 (3 - 1)$ m.
1 mark

Answer: Height of tower $= 20 (3 - 1)$ m $\approx 14.64$ m

Where the marks are

Draws a correct labelled figure (1 mark)
Uses $tan 4 5^{\circ} = 20/ x$ (1 mark)
Obtains $x = 20$ m (½ mark)
Uses $tan 6 0^{\circ} = (h + 20) / x$ (1 mark)
Gets $h + 20 = x 3$ (½ mark)
Finds $h = 20 (3 - 1)$ 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 paper2024 board paper, set 30/3/1 (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 2024: question 34

Hints

Step-by-step solution

Revise the chapter

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