Discussion
The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
Answer: A
Height and shadow are the two legs of the right triangle formed by the sun's ray, and the angle of elevation \( \theta \) sits at the tip of the shadow.
\[ \tan\theta = \frac{\text{height of tree}}{\text{length of shadow}} \]
The two are equal, so the ratio is 1:
\[ \tan\theta = 1 \quad\Longrightarrow\quad \theta = 45^{\circ} \]
No length is needed - only the ratio matters, which is why the question can omit the tree's actual height. At \( 30^{\circ} \) the shadow would be \( \sqrt{3} \) times the height; at \( 60^{\circ} \), \( \tfrac{1}{\sqrt{3}} \) of it.
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