The shadow of a tower is `sqrt(3)` times its height .Then the angle of elevation of the top of the tower is

Options

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

Answer

To solve the problem, we need to find the angle of elevation of the top of the tower given that the shadow of the tower is \(\sqrt{3}\) times its height.

### Step-by-Step Solution:

1. **Define Variables:**
Let the height of the tower be \( h \). According to the problem, the length of the shadow is \(\sqrt{3} \times h\).

2. **Identify the Right Triangle:**
We can visualize a right triangle where:
- The height of the tower (perpendicular) is \( h \).
- The length of the shadow (base) is \(\sqrt{3} \times h\).
- The angle of elevation from the end of the shadow to the top of the tower is \(\theta\).

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

4. **Simplify the Expression:**
Simplifying the expression, we get:
\[ \tan(\theta) = \frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} \]

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

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

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