3-4-5 Right Triangle that loses its 'right-ness'

We all know the 3-4-5 right triangle. But what if we could alter the angle? Drag point F around and observe what happens to the third (green) side. Can you come up with an expression that represents the length of this third side? (Try drawing your own version on paper) There is a small hint available, but only click if you've really thought it through.