implicitly calculate a nodes coordinates from edge length

Hi.

I'm not sure where to post this best. I guess you guys have a good
knowledge in what I seek.

I have a couple of nodes without any coordinates in a database.
I also have all the edges between these nodes with geographic
distances.

I could find real coordinates for certain nodes if I want to, but I
have 2000 records...

Is there some tool that takes the weighted edges and the coordinates
of SOME nodes to calculate the rest of the coordinates?

Example
Given coordinates of 3 nodes, lengths of three edges from these nodes
to node x:
a(0,0), b(1,0), c(0,1), a-x(1.4), b-x(1), c-x(1)

there is only one solution for x, that is x(1,1)

If a-x was not known, it could also have been x(0,0)

I hope you understand what I mean. Does some tool/librarie like this
exist?