How to find network configuration with only line lengths

[LanoYado]

Hi everyone, 

I have a network with 14 nodes and 20 lines. The data are old and there are no xy locations for the nodes, but the lengths (distances) between all these node are known. 

Let's forget the xy locations. Now, with these available data, can we find a way to draw the network (all lines and nodes keep same original angles and proportional lengths) even with different new xy locations of nodes? Is there an engineering idea to find these new xy locations that keep the same shape of original network with no change? 

Thanks in advance

[DanPatterson_Retired]

parallel link here... https://community.esri.com/thread/183563-if-i-know-the-distance-between-nodes-with-two-known-xy-node... not necessarily a NA question