Discussion
To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and he is 5 m away from the wall, what i
Answer: C
The angles are taken from the man's eye, 180 cm = 1.8 m above the ground, and he stands 5 m from the wall.
Window bottom at \( 45^{\circ} \):
\[ 1.8 + 5\tan 45^{\circ} = 1.8 + 5 = 6.8 \text{ m} \]
Window top at \( 60^{\circ} \):
\[ 1.8 + 5\tan 60^{\circ} = 1.8 + 5\sqrt{3} = 1.8 + 8.66 = 10.46 \text{ m} \]
\[ \text{window length} = 10.46 - 6.8 = 3.66 \approx 3.65 \text{ m} \]
The eye height appears in both and cancels in the subtraction, so it affects the individual heights but not the window's length.
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