The problem with his "mathematics" is that if you assume the earth is flat and do this from different latitudes on the earth simultaneously (so that the sun is over the same spot on the earth) you get different values for the altitude of the sun. Since the sun cannot be at different altitudes at the same time, either math just does not work and we need to throw it out (of course it does work, so we can't throw it out), or the earth is not flat.
It was precisely to patch up results like this in a desperate effort to hold onto the notion of a flat earth that the geniuses around here invented EA, AKA "Bendy Light". Did you ever read the wiki?