The angle of elevation of the sun, when the length of the shadow of a tree is \(\sqrt{3}\) times the height of the tree, is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30°
The tree, its shadow and the sun’s ray through the top of the tree form a right-angled triangle. The angle of elevation of the sun is the angle at the tip of the shadow, and its tangent is the height divided by the shadow.
Let the height be \(h\); the shadow is \(\sqrt{3}\,h\)
\(\tan\theta=\displaystyle\frac{h}{\sqrt{3}\,h}=\frac{1}{\sqrt{3}}\)
\(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), so \(\theta=\) 30°