Question

If the length of shadow of a tower on the plane ground is \( \sqrt{3} \) times of its height, the angle of elevation of the sun is:

• A. 60°
• B. 45°
• C. 30°
• D. 90°

Hint:

In right-angled triangles, the tangent of the angle of elevation is the ratio of the height of the object to the length of its shadow.

Answer 1

The Correct Option is C

Let the height of the tower be \( h \) and the length of its shadow be \( \sqrt{3}h \). In this case, we have a right-angled triangle
where:
- The opposite side is the height \( h \), - The adjacent side is the length of the shadow \( \sqrt{3}h \), - The angle of elevation of the sun is \( \theta \). The tangent of the angle of elevation is given by: \[ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\sqrt{3}h} \] Simplifying: \[ \tan \theta = \frac{1}{\sqrt{3}} \]
Step 1: Find the angle of elevation.
We know that: \[ \tan 30^\circ = \frac{1}{\sqrt{3}} \] Therefore, the angle of elevation is \( 30^\circ \).
Step 2: Conclusion.
Thus, the angle of elevation of the sun is 30°.