Perspective: Why Don't Sunbeams Look Parallel?

Not too long ago, I had an internet run-in with a "flat Earth" type who hit me with an argument I'd never heard before: the sun, they insisted, is actually only a few hundred miles from Earth, as can be proven with some simple mathematical analysis of sunbeams. By measuring the apparent angle between sunbeams striking the opposite sides of a valley that they knew the width of, they could trace back and use geometry to calculate how far away the source must be! I want to share this little anecdot...