CUET UG 2025 — General Test Geometry

2025mcqmedium

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Official previous-year question

Held on 23 May 2025 · Verified 13 Jul 2026.

Options

A
10 m
B
20/3 m
C
50/3 m
D
40/3 m

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Solution

Let the height of the building be $h$ m and the distance between the building and tower be $d$ m.

The tower height is 50 m.

From the foot of the tower, the angle of elevation to the top of the building is 30°.

$\tan(30°) = \frac{h}{d}$

$\frac{1}{\sqrt{3}} = \frac{h}{d}$

$d = h\sqrt{3}$ ... (1)

From the foot of the building, the angle of elevation to the top of the tower is 60°.

$\tan(60°) = \frac{50}{d}$

$\sqrt{3} = \frac{50}{d}$

$d = \frac{50}{\sqrt{3}}$ ... (2)

The distance $d$ is the same in both cases. Equating (1) and (2):

$h\sqrt{3} = \frac{50}{\sqrt{3}}$

$h \times \sqrt{3} \times \sqrt{3} = 50$

$h \times 3 = 50$

$h = \frac{50}{3}$

Therefore, the height of the building is $\frac{50}{3}$ m.

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Solution

Let the height of the building be $h$ m and the distance between the building and tower be $d$ m.

The tower height is 50 m.

From the foot of the tower, the angle of elevation to the top of the building is 30°.

$\tan(30°) = \frac{h}{d}$

$\frac{1}{\sqrt{3}} = \frac{h}{d}$

$d = h\sqrt{3}$ ... (1)

From the foot of the building, the angle of elevation to the top of the tower is 60°.

$\tan(60°) = \frac{50}{d}$

$\sqrt{3} = \frac{50}{d}$

$d = \frac{50}{\sqrt{3}}$ ... (2)

The distance $d$ is the same in both cases. Equating (1) and (2):

$h\sqrt{3} = \frac{50}{\sqrt{3}}$

$h \times \sqrt{3} \times \sqrt{3} = 50$

$h \times 3 = 50$

$h = \frac{50}{3}$

Therefore, the height of the building is $\frac{50}{3}$ m.

CUET UG 2025 — General Test Geometry

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry