Discussion
When height of a tree is equal to the length of its shadow, what is the angle of elevation of the sun?
Answer: D
The tower, its shadow and the sun's ray form a right triangle, with the angle of elevation \( \theta \) at the tip of the shadow.
\[ \tan\theta = \frac{\text{height}}{\text{shadow}} \]
Here the height equals the shadow, so the ratio is 1:
\[ \tan\theta = 1 \quad\Longrightarrow\quad \theta = 45^{\circ} \]
It is worth memorising the three standard cases: shadow longer than the height means the sun is low (\( 30^{\circ} \) when the shadow is \( \sqrt{3} \) times the height), equal means \( 45^{\circ} \), and shadow shorter means the sun is high (\( 60^{\circ} \) when the height is \( \sqrt{3} \) times the shadow).
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