You’re tasked with constructing a greenhouse with a glass, arc-shaped ceiling. You want the sun to shine through the ceiling
as long as possible while still making it high enough to fit your taller
plants. You determine the best angle of elevation from the center to the
wall tops to be formed to be θ=pi/3, and that you can afford to make the
front wall 8 ft wide.
1) At what height does the ceiling touch the side walls?
2) How long would the ceiling arc measure from the entrance
perspective?