CUET UG 2025 — General Test Geometry

2025mcqmedium

An observer 2 m tall is 24 $\sqrt{3}$ m away from a building. The angle of elevation of the top of the building as seen by him is 30°. What is the height of the building?

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

A
24 m
B
20 m
C
30 m
D
26 m

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Solution

The observer is 2 m tall and stands 24√3 m away from the building. The angle of elevation to the top of the building is 30°.

The angle of elevation is measured from the observer's eye level, not from the ground. Let the total height of the building be $H$ meters.

The height of the building above eye level is $(H - 2)$ meters.

Using the tangent ratio:

$\tan(30°) = \frac{\text{opposite}}{\text{adjacent}}$

$\tan(30°) = \frac{H - 2}{24\sqrt{3}}$

Since $\tan(30°) = \frac{1}{\sqrt{3}}$ :

$\frac{1}{\sqrt{3}} = \frac{H - 2}{24\sqrt{3}}$

Cross multiplying:

$1 \times 24\sqrt{3} = (H - 2) \times \sqrt{3}$

$24\sqrt{3} = (H - 2) \times \sqrt{3}$

Dividing both sides by $\sqrt{3}$ :

$24 = H - 2$

$H = 26$

Therefore, the height of the building is 26 m.

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Solution

The observer is 2 m tall and stands 24√3 m away from the building. The angle of elevation to the top of the building is 30°.

The angle of elevation is measured from the observer's eye level, not from the ground. Let the total height of the building be $H$ meters.

The height of the building above eye level is $(H - 2)$ meters.

Using the tangent ratio:

$\tan(30°) = \frac{\text{opposite}}{\text{adjacent}}$

$\tan(30°) = \frac{H - 2}{24\sqrt{3}}$

Since $\tan(30°) = \frac{1}{\sqrt{3}}$ :

$\frac{1}{\sqrt{3}} = \frac{H - 2}{24\sqrt{3}}$

Cross multiplying:

$1 \times 24\sqrt{3} = (H - 2) \times \sqrt{3}$

$24\sqrt{3} = (H - 2) \times \sqrt{3}$

Dividing both sides by $\sqrt{3}$ :

$24 = H - 2$

$H = 26$

Therefore, the height of the building is 26 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