The length of the shadow of a vertical pole is `1/sqrt3` times its height. Find the angle of elevation .

Options

A. `60^0`
B. `45^0`
C. `90^0`
D. `30^0`

Explanation

To solve the problem, we will use the relationship between the height of the pole, the length of its shadow, and the angle of elevation.

### 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. **Identify the Right Triangle:**
In the right triangle formed by the pole, the shadow, and the line of sight from the top of the pole to the end of the shadow, we have:
- The height of the pole \( h \) as the opposite side.
- The length of the shadow \( s \) as the adjacent side.
- The angle of elevation \( \theta \) from the tip of the shadow to the top of the pole.

3. **Use the Tangent Function:**
The tangent of the angle of elevation \( \theta \) is given by the ratio of the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{s} \]

4. **Substitute the Length of the Shadow:**
Substitute \( s \) from step 1 into the tangent function:
\[ \tan(\theta) = \frac{h}{\frac{1}{\sqrt{3}} h} \]
Simplifying this gives:
\[ \tan(\theta) = \frac{h \cdot \sqrt{3}}{h} = \sqrt{3} \]

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

### Conclusion:
The angle of elevation of the top of the pole is \( 60^\circ \).