Question

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

• A. \(45^\circ\)
• B. \(30^\circ\)
• C. \(60^\circ\)
• D. \(0^\circ\)

Hint:

Memorize standard angle-triangle ratios for \(\theta = 30^\circ, 45^\circ, 60^\circ\) to solve shadow problems quickly.

Answer 1

The Correct Option is B

Given:
Length of shadow of a tower = \(\sqrt{3}\) times its height.

Step 1: Let the height of tower = \(h\)
Length of shadow = \(\sqrt{3} \, h\)

Step 2: Use right triangle trigonometry
The angle of elevation of the sun is \(\theta\).
\[ \tan \theta = \frac{\text{height}}{\text{shadow}} = \frac{h}{\sqrt{3} \, h} = \frac{1}{\sqrt{3}} \]

Step 3: Find \(\theta\) from \(\tan \theta = \frac{1}{\sqrt{3}}\)
\[ \tan 30^\circ = \frac{1}{\sqrt{3}} \] So, \[ \theta = 30^\circ \]

Final Answer:
\[ \boxed{30^\circ} \]