The ratio fo the height of a tower and the length of its shadow is `sqrt3 : 1.` Find the angle of elevation of the Sun.

Answer

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

### Step-by-Step Solution:

1. **Understand the Problem**:
We have a tower (AB) and its shadow (BC). The height of the tower (AB) is in the ratio of \(\sqrt{3}\) to the length of the shadow (BC), which is 1.

2. **Set Up the Ratio**:
Let the height of the tower (AB) be \(h\) and the length of the shadow (BC) be \(s\). According to the given ratio:
\[ \frac{h}{s} = \sqrt{3} \]
This implies:
\[ h = \sqrt{3} \cdot s \]

3. **Draw a Right Triangle**:
We can visualize this scenario as a right triangle where:
- AB (height of the tower) is the opposite side,
- BC (length of the shadow) is the adjacent side,
- AC (hypotenuse) is the line from the top of the tower to the tip of the shadow.

4. **Use Trigonometric Ratios**:
The angle of elevation (\(\theta\)) of the Sun can be found using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{AB}{BC} = \frac{h}{s} \]

5. **Substitute the Values**:
We already established that \(h = \sqrt{3} \cdot s\). Therefore:
\[ \tan(\theta) = \frac{\sqrt{3} \cdot s}{s} = \sqrt{3} \]

6. **Find the Angle**:
To find \(\theta\), we need to determine the angle whose tangent is \(\sqrt{3}\). We know from trigonometric values that:
\[ \tan(60^\circ) = \sqrt{3} \]
Thus, we find:
\[ \theta = 60^\circ \]

7. **Conclusion**:
The angle of elevation of the Sun is \(60^\circ\).

### Final Answer:
The angle of elevation of the Sun is \(60^\circ\).