If the height of a tree is \(3\sqrt{3}\) meters and the length of its shadow is 3 meters, find the angle of elevation of the sun.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{\pi}{3}\)
The tree, its shadow and the sun’s ray form a right triangle. The angle of elevation \(\theta\) is at the tip of the shadow, so \(\displaystyle \tan\theta=\frac{\text{height of the tree}}{\text{length of the shadow}}\).
\(\displaystyle \tan\theta=\frac{3\sqrt{3}}{3}=\sqrt{3}\)
\(\tan 60^{\circ}=\sqrt{3}\), so \(\theta=60^{\circ}\), which is \(\frac{\pi}{3}\) in radians
