Discussion
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: B
The angle of elevation \( \theta \) satisfies
\[ \tan\theta = \frac{\text{height of tree}}{\text{length of shadow}} \]
Here the shadow is \( \sqrt{3} \) times the height, so with height \( h \):
\[ \tan\theta = \frac{h}{\sqrt{3}\,h} = \frac{1}{\sqrt{3}} \]
\[ \theta = 30^{\circ} \]
The tree's actual height cancels, so it is never needed. Inverting the ratio gives \( \tan\theta = \sqrt{3} \) and hence 60° - the mirror-image case, where the shadow is shorter than the tree.
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