If the length of the shadow of a tower is `sqrt(3)` times its height of then the angle of elevation of the sun is

Options

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

Answer

To solve the problem, we need to use the relationship between the height of the tower, the length of its shadow, and the angle of elevation of the sun. Let's denote:

- Height of the tower = h
- Length of the shadow = L
- Angle of elevation of the sun = θ

According to the problem, the length of the shadow (L) is given as \( \sqrt{3} \) times the height of the tower (h). Therefore, we can write:

\[ L = \sqrt{3} \cdot h \]

Now, we can use the tangent function to find the angle of elevation (θ). The tangent of the angle of elevation is given by the ratio of the opposite side (height of the tower) to the adjacent side (length of the shadow):

\[ \tan(θ) = \frac{\text{height of the tower}}{\text{length of the shadow}} \]

Substituting the values we have:

\[ \tan(θ) = \frac{h}{\sqrt{3} \cdot h} \]

The height (h) cancels out:

\[ \tan(θ) = \frac{1}{\sqrt{3}} \]

Now, we need to find the angle θ for which the tangent is \( \frac{1}{\sqrt{3}} \). From trigonometric ratios, we know:

\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]

Therefore, we can conclude:

\[ θ = 30^\circ \]

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