Discussion
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?
Answer: D
Join the two chimney tops. The horizontal leg of that line is the gap between the houses, and its vertical leg is the difference in their heights:
\[ 25 - 10 = 15 \text{ m} \]
The line makes 45° with the ground, and \( \tan 45^{\circ} = 1 \), so the two legs are equal:
\[ \tan 45^{\circ} = \frac{15}{d} = 1 \quad\Longrightarrow\quad d = 15 \text{ m} \]
The trap is using the sum 35 m or one height alone; only the height difference lies opposite the 45° angle.
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