The ratio of the length of a rod and its shadow is `1:sqrt(3)` .The angle of elevationn of the sun is :

Options

A. `90^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to find the angle of elevation of the sun given the ratio of the length of a rod to its shadow is \(1:\sqrt{3}\).

### Step-by-Step Solution:

1. **Understanding the Ratio**:
- Let the length of the rod be \(h\) (the height of the rod) and the length of its shadow be \(s\).
- According to the problem, the ratio of the length of the rod to its shadow is given as:
\[ \frac{h}{s} = \frac{1}{\sqrt{3}} \]

2. **Expressing Lengths**:
- From the ratio, we can express the lengths in terms of a variable \(x\):
\[ h = x \quad \text{and} \quad s = \sqrt{3}x \]

3. **Identifying the Right Triangle**:
- In the right triangle formed by the rod and its shadow, the height of the rod is the opposite side, and the shadow is the adjacent side.
- Therefore, we can apply the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{s} \]

4. **Substituting the Values**:
- Substitute \(h\) and \(s\) into the tangent function:
\[ \tan(\theta) = \frac{x}{\sqrt{3}x} \]
- Simplifying this gives:
\[ \tan(\theta) = \frac{1}{\sqrt{3}} \]

5. **Finding the Angle**:
- We know that:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
- Therefore, we can conclude:
\[ \theta = 30^\circ \]

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

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