The angle of elevation of the sun when the length of the shadow of a pole is `sqrt(3)` times the height of the pole is

Options

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

Answer

To solve the problem, we need to determine the angle of elevation of the sun when the length of the shadow of a pole is \(\sqrt{3}\) times the height of the pole.

### Step-by-Step Solution:

1. **Define Variables:**
Let the height of the pole be \(h\). According to the problem, the length of the shadow \(s\) is given by:
\[ s = \sqrt{3} \cdot h \]

2. **Use Trigonometric Ratios:**
The angle of elevation of the sun, denoted as \(\theta\), can be related to the height of the pole and the length of the shadow using the tangent function:
\[ \tan(\theta) = \frac{\text{height of the pole}}{\text{length of the shadow}} = \frac{h}{s} \]

3. **Substitute the Length of the Shadow:**
Substitute \(s\) in the equation:
\[ \tan(\theta) = \frac{h}{\sqrt{3} \cdot h} \]
Simplifying this gives:
\[ \tan(\theta) = \frac{1}{\sqrt{3}} \]

4. **Find the Angle \(\theta\):**
We know from trigonometric values that:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
Therefore, we can conclude that:
\[ \theta = 30^\circ \]

### Final Answer:
The angle of elevation of the sun when the length of the shadow of a pole is \(\sqrt{3}\) times the height of the pole is \(30^\circ\).