So this is basically a proof basic trigonometry is true (as I pointed out in the Reddit title). Honestly, I never really understood why everybody assumed/accepted this as intuitive; I found it to be a relatively huge leap in logic and counter-intuitive, so I thought up this proof myself.

One thing to note is the choice of direction. I mention lining them up vertically , but there is no reason to take this specific direction. As long as they are the same in one direction, it is fine, but I wrote up vertical to avoid becoming unnecessarily verbose.