Third point of a triangle from only two points and all three edge lengths

I want a triangle composed of points A, B and C in Cartesian 3D space.

I currently know the positions of points A and B, but I need point C. I have the line segment AB, and thus its magnitude. I have only the magnitudes of line segments AC and BC.

From this data, how do I derive point C? Please explain your logic. Thank you for your help.

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If I understand the question correctly, it is not uniquely determined. –  Pandora Mar 25 '11 at 17:32
There are an infinite amount of possible point C's. Imagine the intersection of two spheres of radius $|AC|$ coming from point $A$ and radius $|BC|$ coming from point $B$. –  Justin L. Mar 25 '11 at 17:33
its only defined up to a rotation...you can use the law of cosines to get the angles –  yoyo Mar 25 '11 at 17:34