If the length of shadow of a vertical pole on the horizontal ground is `sqrt3` times of its height, then the angles of elevation of sun is :

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to find the angle of elevation of the sun given that the length of the shadow of a vertical pole is \(\sqrt{3}\) times its height. Let's denote the height of the pole as \(h\).

### Step-by-Step Solution:

1. **Identify the Relationship**:
- Let the height of the pole be \(h\).
- The length of the shadow is given as \(\sqrt{3} \times h\).

2. **Set Up the Right Triangle**:
- In the right triangle formed by the pole, the shadow, and the line from the top of the pole to the tip of the shadow, we have:
- Opposite side (height of the pole) = \(h\)
- Adjacent side (length of the shadow) = \(\sqrt{3}h\)

3. **Use the Tangent Function**:
- The tangent of the angle of elevation \(\theta\) is defined as the ratio of the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{\sqrt{3}h} \]
- Simplifying this gives:
\[ \tan(\theta) = \frac{1}{\sqrt{3}} \]

4. **Find the Angle**:
- To find \(\theta\), we need to determine which angle has a tangent of \(\frac{1}{\sqrt{3}}\).
- From trigonometric ratios, we know:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
- Therefore, \(\theta = 30^\circ\).

5. **Conclusion**:
- The angle of elevation of the sun is \(30^\circ\).

### Final Answer:
The angle of elevation of the sun is \(30^\circ\).

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