A man stands at the end point of the shadow of a pole. He measure that length of shadow is `1/sqrt(3)` times that of pole. What is the Sun's altitude ?

Options

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

Answer

To solve the problem, we need to find the altitude of the sun based on the given information about the pole and its shadow.

### Step-by-Step Solution:

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

2. **Use the Tangent Function**:
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 Shadow Length**:
Substitute \( s \) from step 1 into the tangent function:
\[ \tan(\theta) = \frac{h}{\frac{1}{\sqrt{3}} h} \]

4. **Simplify the Expression**:
The \( h \) in the numerator and denominator cancels out:
\[ \tan(\theta) = \frac{h}{\frac{1}{\sqrt{3}} h} = \sqrt{3} \]

5. **Find the Angle**:
We know that \( \tan(60^\circ) = \sqrt{3} \). Therefore, we can conclude:
\[ \theta = 60^\circ \]

6. **Final Answer**:
The altitude of the sun is \( 60^\circ \).