Yes, this is really good and simple.
You have any these type simple solutions please provide
My best guess is that we don't have enough information to solve this.
k4 is an angle whose numerical value we know.
k3 is the square of a length whose value we know
k1 is the reciprical of cos k4, so just another numerical value we know
k2 (he's there) is a known length divided by the sinus of a known angle, so just another numerical value we know.
I've looked at the link to the polynomial approach, I can't quite see how to get round the fact that I have an A and the square root of A+constant.