Prove that in polar coordinates for any given point P on the curve $\displaystyle r=f(\theta)$, the angle $\displaystyle \omega$ from the radius vector CP to the tangent line at P is given by $\displaystyle tan(\omega) = \frac{r}{r'}$

I understand the proof given here if we assume the given lengths, but I can't make out the diagram and I don't understand why the given lengths are true; why PR = $\displaystyle \rho sin(\Delta \theta)$ for instance. Could someone provide a better diagram or explain it? Thanks.

http://wstein.org/home/wdj/teaching/...us_vector.html