Discussion

When the sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

Answer: B

Let the tower be \( h \) m. The shadow shortens as the sun rises.

\[ s_{30} = \frac{h}{\tan 30^{\circ}} = h\sqrt{3}, \qquad s_{60} = \frac{h}{\tan 60^{\circ}} = \frac{h}{\sqrt{3}} \]

\[ h\sqrt{3} - \frac{h}{\sqrt{3}} = 70 \quad\Longrightarrow\quad \frac{3h - h}{\sqrt{3}} = 70 \]

\[ \frac{2h}{\sqrt{3}} = 70 \quad\Longrightarrow\quad h = 35\sqrt{3} = 60.62 \approx 60.6 \text{ m} \]

70 m is the decrease, not a shadow length. Mistaking it for one gives either 140 m or 35 m - hence those distractors.

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