Prepare shadow maps for point \(\mathrm{P}\) on the sun-path diagrams for \(35^{\circ} \mathrm{N}\) and \(40^{\circ} \mathrm{N}\) for the following three geometries shown in a, b, and c. Determine the hours of shading that occur each month.

P 45 40 50 (a) South (b) |3 45 30 P 30 45 60 -30 South (c) South