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

Let the height of the tower be \( h \), and the length of the shadow be \( \sqrt{3}h \). Using trigonometry: \[ \tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}} = \dfrac{h}{\sqrt{3}h} = \dfrac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ \]