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'Raising the Roof' printed from http://nrich.maths.org/

The diagram shows a crosssectional 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.

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, $a$.