If the ratio of the height of a tower and the length of its shasdow is `sqrt(3):1`, then the angle of elevation of the Sun is `30^(@)`. Is is true or false?

Answer

To determine whether the statement is true or false, we will analyze the given information step by step.

### Step-by-Step Solution:

1. **Understanding the Given Ratio**:
- We are given that the ratio of the height of the tower (h) to the length of its shadow (s) is \(\sqrt{3}:1\).
- This can be expressed mathematically as:
\[ \frac{h}{s} = \sqrt{3} \]

2. **Using the Angle of Elevation**:
- The angle of elevation of the Sun is given as \(30^\circ\).
- In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the opposite side (height of the tower) to the adjacent side (length of the shadow):
\[ \tan(30^\circ) = \frac{h}{s} \]

3. **Calculating \(\tan(30^\circ)\)**:
- We know that:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]

4. **Setting Up the Equation**:
- From the tangent definition, we can set up the equation:
\[ \frac{h}{s} = \tan(30^\circ) = \frac{1}{\sqrt{3}} \]

5. **Comparing the Two Ratios**:
- We have two expressions for \(\frac{h}{s}\):
- From the ratio given: \(\frac{h}{s} = \sqrt{3}\)
- From the tangent of the angle: \(\frac{h}{s} = \frac{1}{\sqrt{3}}\)
- These two values are not equal:
\[ \sqrt{3} \neq \frac{1}{\sqrt{3}} \]

6. **Conclusion**:
- Since the two ratios are not equal, the statement that the angle of elevation of the Sun is \(30^\circ\) when the ratio of the height of the tower to the length of its shadow is \(\sqrt{3}:1\) is **false**.

### Final Answer:
**False**