Calculate width and height of a rectangle, given its diagonal and ratio Well, I know, it's easy. We did it in class some time ago and I forgot it, I'm stupid because I can't figure it out:
E.g. I have a 32" TV with 16:9 ratio and I want to know its width and height.
I'd like to know the whole derivation so I can understand it (again) ...
Enlightenment, please! Thanks.

$$w^2+h^2=32^2,\\\frac wh=\frac{16}{9}.$$
Then dividing by $h^2$,
$$\frac{w^2}{h^2}+1=\frac{16^2}{9^2}+1=\frac{32^2}{h^2},$$
$$h=\frac{32\cdot9}{\sqrt{16^2+9^2}},w=\frac{16}9h.$$
