Discussion
If the elevation of the sun changed from 30º to 60º, then find the difference between the lengths of shadows of a pole 15 m high, made at these two positions.
Answer: C
Compute both shadow lengths for the 15 m pole and subtract.
\[ s_{30} = \frac{15}{\tan 30^{\circ}} = 15\sqrt{3} \text{ m} \]
\[ s_{60} = \frac{15}{\tan 60^{\circ}} = \frac{15}{\sqrt{3}} = 5\sqrt{3} \text{ m} \]
\[ \text{difference} = 15\sqrt{3} - 5\sqrt{3} = 10\sqrt{3} \approx 17.3 \text{ m} \]
Writing \( \tfrac{15}{\sqrt{3}} \) as \( 5\sqrt{3} \) puts both terms in the same surd, so they subtract directly.
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