Discussion
An electric pole, 14 metres high, casts a shadow of 10 metres. What will be the height of a tree that casts a shadow of 15 metres under similar conditions ?
Answer: A
The tree is 21 m high.
Under similar conditions the sun's rays fall at the same angle, so heights are proportional to the shadows they cast (similar triangles):
\[ \begin{aligned} \frac{h}{15} &= \frac{14}{10} \\ h &= \frac{14 \times 15}{10} = 21\ \text{m} \end{aligned} \]
The shadow is 1.5 times longer, so the tree is 1.5 times taller than the pole. 14 m is the pole itself, 15 m merely repeats the shadow length, and 25 m comes from adding the 10 m difference instead of scaling.
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