Can I find the magnetic heading from A to B on triangle ABC if the lengths and angles inside the triangle are known?

I want to find the magnetic heading (from north) from a point $A$ to a point $B$ on a $\triangle ABC$. $A, B and C$ are moving and so the angles can be any value. as an example, the triangle could be this shape.

Lengths $a, b$ and $c$ are known and therefore using the law of cosines the angles at A, B and C can be found. Is there a way to use these values to find the magnetic heading or is it completely removed from these angles?

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No, the heading cannot be found from the information provided. Think of it this way: The triangle in your example could be rotated by any amount from 0 to 2Pi without changing the side lengths or angles. –  Pieter Geerkens Apr 22 '13 at 22:20
If you know the $(x,y)$ coordinates of each point, then you can find it –  Quincunx Apr 22 '13 at 22:25