How is this angle relation true? 
Either I'm silly and I'm missing something very simple, or my text book is incorrect. I'm trying to verify a line in the text book which claims that sin(a) = s/r. I can't seem to prove this to myself and its infuriating.

Let $x$ be the angle (in the triangle) that is opposite to side $s$. Then $a+x=180^\circ$. 
It is clear that $\sin x=\frac{s}{r}$. But if two angles add up to $180^\circ$, their sines are the same. So 
$$\sin a=\sin x=\frac{s}{r}.$$
