Discussion
The heights of two poles are 80 m and 62.5 m. If the line joining their tops makes an angle of 45º with the horizontal, then find the distance between the poles.
Answer: D
Join the two tops. That line's vertical leg is the height difference and its horizontal leg is the gap between the poles.
\[ \text{height difference} = 80 - 62.5 = 17.5 \text{ m} \]
\[ \tan 45^{\circ} = \frac{17.5}{d} = 1 \quad\Longrightarrow\quad d = 17.5 \text{ m} \]
At \( 45^{\circ} \) the two legs are always equal, so the distance simply is the height difference. Using either height on its own, or their sum, is where the other options come from.
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