CUET UG 2025 — General Test Geometry

2025mcqmedium

From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?

Official previous-year question

Held on 28 May 2025 · Verified 13 Jul 2026.

Options

A
30 m
B
33 m
C
35 m
D
38 m

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Solution

Let the building height be 78 m, the tower height be $h$ m, and the horizontal distance between them be $d$ m.

The angle of depression to the bottom of the tower is 45°.

The angle of depression to the top of the tower is 30°.

For the angle of depression to the bottom of the tower:

$\tan(45°) = \frac{78}{d}$

$1 = \frac{78}{d}$

$d = 78$ m

For the angle of depression to the top of the tower, the vertical distance from the top of the building to the top of the tower is $(78 - h)$ m.

$\tan(30°) = \frac{78 - h}{d}$

$\frac{1}{\sqrt{3}} = \frac{78 - h}{78}$

$78 - h = \frac{78}{\sqrt{3}}$

$78 - h = \frac{78}{1.732}$

$78 - h = 45.03$

$h = 78 - 45.03$

$h = 33$ m

Therefore, the height of the tower is approximately 33 m.

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Solution

Let the building height be 78 m, the tower height be $h$ m, and the horizontal distance between them be $d$ m.

The angle of depression to the bottom of the tower is 45°.

The angle of depression to the top of the tower is 30°.

For the angle of depression to the bottom of the tower:

$\tan(45°) = \frac{78}{d}$

$1 = \frac{78}{d}$

$d = 78$ m

For the angle of depression to the top of the tower, the vertical distance from the top of the building to the top of the tower is $(78 - h)$ m.

$\tan(30°) = \frac{78 - h}{d}$

$\frac{1}{\sqrt{3}} = \frac{78 - h}{78}$

$78 - h = \frac{78}{\sqrt{3}}$

$78 - h = \frac{78}{1.732}$

$78 - h = 45.03$

$h = 78 - 45.03$

$h = 33$ m

Therefore, the height of the tower is approximately 33 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