Geometry

Trigonometry

Easy

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:

$30^o$

$45^o$

$60^o$

$90^o$

✅ Correct Option: 3

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:

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

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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Solution

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CUET General Test Past Year Questions (Topic-Wise)

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: