The length of a vertical rod and its shadow are in the ratio of 2:√12. Find the angle of elevation of the sun.

75°

45°

60°

30°

APEDIA

NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

The length of a vertical rod and its shadow are in the ratio of 2:√12. Find the angle of elevation of the sun.

Correct Answer

30°

[Trigonometric Setup]: The physical scenario forms a classic right-angled triangle where the vertical rod acts as the 'perpendicular' (height) and the shadow ca......

💡 Analysis & Explanation

[Trigonometric Setup] ▼

The physical scenario forms a classic right-angled triangle where the vertical rod acts as the 'perpendicular' (height) and the shadow cast on the ground forms the 'base'.

[Ratio Integration] ▼

The problem provides the ratio of Perpendicular to Base as 2 : √12. In trigonometry, the ratio of Perpendicular/Base defines the Tangent of the angle of elevation (tan θ).

[Radical Simplification] ▼

We can mathematically simplify the radical in the denominator: √12 can be factored into √(4 × 3), which simplifies perfectly to 2√3. Therefore, the ratio becomes 2 / 2√3.

[Final Angle Deduction] ▼

Canceling the common factor of 2 from the numerator and denominator leaves us with tan θ = 1 / √3. Looking at standard trigonometric tables, the angle whose tangent is 1/√3 is precisely 30 degrees.

Conclusion ▼

The required angle of elevation is 30°.

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The length of a vertical rod and its shadow are in the ratio of 2:√12. Find the angle of elevation of the sun.