The angle of elevation of the sun, when the length of the shadow of a tower is \(1/\sqrt{3}\) times the height of the tower, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60°
The tower, its shadow and the sun’s ray over the top of the tower form a right triangle. The angle of elevation \(\theta\) of the sun is at the tip of the shadow, and \(\tan\theta=\frac{\text{height of the tower}}{\text{length of the shadow}}\).
The angle (for a tower of height \(h\) the shadow is \(h/\sqrt{3}\), so the \(h\) cancels):
\(\displaystyle \tan\theta=\frac{h}{h/\sqrt{3}}=\sqrt{3}\)
\(\tan60^\circ=\sqrt{3}\), so \(\theta=60^\circ\)