Thank you for the restatement of the problem, that is much more forward and condensed. I was hoping that, yes, there would be some clever equation, that with enough crunching would fall out and I could simply plug in a set of measurements and always know the tenth distance. It seems that there...
A way to imagine this problem to stand on a plane. You have chosen three points on that plane to create a triangle-base and from these three points you can make distance measurements in any direction. You know the distance between each of the three points of the base, but you do not yet know...