Discussion
The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45º to 30º. Find the height of the tower, correct to two decimal places.
Answer: B
The shadow lengthens as the sun drops from \( 45^{\circ} \) to \( 30^{\circ} \).
\[ s_{45} = \frac{h}{\tan 45^{\circ}} = h, \qquad s_{30} = \frac{h}{\tan 30^{\circ}} = h\sqrt{3} \]
\[ h\sqrt{3} - h = 10 \quad\Longrightarrow\quad h(\sqrt{3}-1) = 10 \]
\[ h = \frac{10}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} = \frac{10(\sqrt{3}+1)}{2} = 5(\sqrt{3}+1) \]
\[ h = 5 \times 2.732 = 13.66 \text{ m} \]
The 10 m is the increase in shadow, not a shadow length in its own right.
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