If the height of a pole is 8√3 meters… - CUET UG 2025 General Test PYQ

CUET UG 2025 — General Test Geometry

2025mcqeasy

If the height of a pole is $8\sqrt{3}$ meters and the length of its shadow is 8 meters, then the angle of elevation of the sun is:

Official previous-year question

Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
$30^o$
B
$45^o$
C
$60^o$
D
$90^o$

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Solution

A pole of height $8\sqrt{3}$ meters casts a shadow of length 8 meters. This creates a right triangle where:

The pole is the vertical side (opposite) = $8\sqrt{3}$ meters
The shadow is the horizontal side (adjacent) = $8$ meters
The angle between the ground and the sun's ray is $\theta$

Since we know the opposite and adjacent sides, we use the tangent ratio:

$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\text{Height of pole}}{\text{Length of shadow}}$

Substituting the values:

$\tan(\theta) = \frac{8\sqrt{3}}{8}$

Simplifying:

$\tan(\theta) = \sqrt{3}$ <hr> From standard trigonometric values: - $\tan(30°) = \frac{1}{\sqrt{3}}$ - $\tan(45°) = 1$ - $\tan(60°) = \sqrt{3}$ Since $\tan(\theta) = \sqrt{3}$:$ \theta = 60°$

Therefore, the angle of elevation of the sun is $60°$ .

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