Even looking on the Wiki pages I have a hard time figuring this one out.
But why does SOH CAH TOA hold? As in, why is $\sin(x)$ the same as the opposite over hypotenuse of a right triangle? Why is $\cos(x)$ the adjacent over hypotenuse? Why is $\tan(x)$ the opposite over the adjacent? And why don't any of these work for right angles as the reference theta?
I understand that these facts are easily used but if I were trying to invent this for the first time I'd be totally lost. I don't understand where these trig functions come from, what their format definitions are, why they're defined this way, where they come from, why they're true, how we know they're true, etc. To me they are mysterious functions that everyone just uses and takes for granted but I have no idea how they work.