Question

If the ratio of the length of a rod and its shadow is \(1 : \sqrt{3}\), the elevation angle of the sun will be

• A. \(30^\circ\)
• B. \(45^\circ\)
• C. \(60^\circ\)
• D. \(90^\circ\)

Hint:

When the shadow is longer than the height, the angle of elevation is less than \(45^\circ\).

Answer 1

The Correct Option is A

Step 1: Represent using tangent.
\[ \tan \theta = \frac{\text{height of rod}}{\text{length of shadow}} = \frac{1}{\sqrt{3}} \]
Step 2: Recall standard trigonometric ratios.
\[ \tan 30^\circ = \frac{1}{\sqrt{3}}, \quad \tan 45^\circ = 1, \quad \tan 60^\circ = \sqrt{3} \]
Step 3: Comparison.
Since \(\tan \theta = \frac{1}{\sqrt{3}}\), we get \(\theta = 30^\circ\).
Step 4: Conclusion.
The elevation angle of the sun is \(30^\circ\).