Integer Solutions to Angle Optimization Problems

Summary: We investigate integer and rational solutions to two angle optimization problems: where to park at a drive-in movie theater and where to place a solar panel in an alley between two walls. For the first problem we parametrize all integer-valued problems with integer solutions, and count the number of integer-valued problems with a given integer solution. For the second problem we characterize all integer-valued problems with rational solutions, and parametrize those solutions that also have a maximum angle that is rational in degrees.