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'Raising the Roof' printed from https://nrich.maths.org/
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The diagram shows a cross-sectional view of a house.
The roof space is 12 metres across and 1.5 metres high at the
highest point in the centre.
Find the angle of slope of the roof.
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Also find the sloping distance $b$ from the top of the roof to
the top of the walls.
The hottest part of the day is when the sun is directly
overhead. The roof overhangs by a distance $a$ and it shades all
the windows from the sun while the sun's rays are inclined at 8
degrees or less to the vertical. The lowest part of the windows is
one metre above the ground and the angle $\phi$ in the diagram is 8
degrees. Find the length of the overhang, $a$.