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: A
Let the tower be \( h \) m. The shadow shortens as the sun climbs.
\[ s_{30} = \frac{h}{\tan 30^{\circ}} = h\sqrt{3}, \qquad s_{60} = \frac{h}{\tan 60^{\circ}} = \frac{h}{\sqrt{3}} \]
\[ h\sqrt{3} - \frac{h}{\sqrt{3}} = 70 \]
\[ \frac{3h - h}{\sqrt{3}} = 70 \quad\Longrightarrow\quad \frac{2h}{\sqrt{3}} = 70 \]
\[ h = 35\sqrt{3} = 35 \times 1.732 = 60.62 \approx 60.6 \text{ m} \]
70 m is the change in the shadow, not a shadow length - using it directly as one of the two lengths gives 140 m or 35 m, which is why both appear as distractors.
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