CUET UG 2025 — General Test Geometry

2025mcqmedium

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower when seen from the foot of the building is 60°. If the tower is 60 m high, then the height of the building is:

Official previous-year question

Held on 16 May 2025 · Verified 13 Jul 2026.

Options

A
35 m
B
20 m
C
25 m
D
30 m

Did you get this right?

Solution

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

Tower height = 60 m

Angle from building's foot to tower's top = 60°

Angle from tower's foot to building's top = 30°

From the foot of the building, looking at the top of the tower:

$\tan(60°) = \frac{60}{d}$

$\sqrt{3} = \frac{60}{d}$

$d = \frac{60}{\sqrt{3}}$

$d = 20\sqrt{3}$ m

From the foot of the tower, looking at the top of the building:

$\tan(30°) = \frac{h}{d}$

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

Substituting $d = 20\sqrt{3}$ :

$\frac{1}{\sqrt{3}} = \frac{h}{20\sqrt{3}}$

$h = \frac{20\sqrt{3}}{\sqrt{3}}$

$h = 20$ m

The height of the building is 20 m.

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Solution

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

Tower height = 60 m

Angle from building's foot to tower's top = 60°

Angle from tower's foot to building's top = 30°

From the foot of the building, looking at the top of the tower:

$\tan(60°) = \frac{60}{d}$

$\sqrt{3} = \frac{60}{d}$

$d = \frac{60}{\sqrt{3}}$

$d = 20\sqrt{3}$ m

From the foot of the tower, looking at the top of the building:

$\tan(30°) = \frac{h}{d}$

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

Substituting $d = 20\sqrt{3}$ :

$\frac{1}{\sqrt{3}} = \frac{h}{20\sqrt{3}}$

$h = \frac{20\sqrt{3}}{\sqrt{3}}$

$h = 20$ m

The height of the building is 20 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