Question

The length of the shadow of a vertical pole is \(\sqrt 3\) times its original length. The angle of elevation to the sun is ____ .

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Answer 1

The Correct Option is A

To solve the problem, we need to find the angle of elevation of the sun when the length of the shadow of a vertical pole is \( \sqrt{3} \) times its height.

1. Understanding the Triangle Formed:
A right-angled triangle is formed by:
- The vertical pole (opposite side),
- The shadow (adjacent side),
- The line from the top of the pole to the tip of the shadow (hypotenuse).
Let the height of the pole be \( h \), then the length of the shadow is \( \sqrt{3}h \).

2. Using the Tangent Function:
The tangent of the angle of elevation \( \theta \) is given by:
\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} \)

3. Finding the Angle:
We know that:
\( \tan(30^\circ) = \frac{1}{\sqrt{3}} \)
Therefore, \( \theta = 30^\circ \)

Final Answer:
The angle of elevation to the sun is 30°.