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 is the length of the window?
Answer: A
Angles are measured from the man's eye, which is 180 cm = 1.8 m above the ground, and he is 5 m from the wall.
Bottom of the window, at 45°:
\[ \text{rise} = 5\tan 45^{\circ} = 5 \text{ m} \quad\Longrightarrow\quad \text{height} = 1.8 + 5 = 6.8 \text{ m} \]
Top of the window, at 60°:
\[ \text{rise} = 5\tan 60^{\circ} = 5\sqrt{3} = 8.66 \text{ m} \quad\Longrightarrow\quad \text{height} = 1.8 + 8.66 = 10.46 \text{ m} \]
\[ \text{window length} = 10.46 - 6.8 = 3.66 \approx 3.65 \text{ m} \]
The 1.8 m appears in both heights and cancels in the subtraction, so the eye height does not actually affect the window's length here - but it is needed if the question asks for either height on its own.
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