CUET UG 2025 — General Test Geometry

A pole of height $8\sqrt{3}$83​ meters casts a shadow of length 8 meters. This creates a right triangle where:

• The pole is the vertical side (opposite) = $8\sqrt{3}$83​ meters
• The shadow is the horizontal side (adjacent) = $8$8 meters
• The angle between the ground and the sun's ray is $\theta$θ

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

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

Substituting the values:

$$\tan(\theta) = \frac{8\sqrt{3}}{8}$$tan(θ)=883​​

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°$

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