# what is the coordinate of the third point in a triangle?

I have a triangle in the Cartesian planeˏ I know the coordinates of only two points of this triangle (none of these two points are on the origin (0,0))ˏ I also know it's sides lengths and all it's angles.

How can I find the coordinates of the third unknown point in this triangle?

Thanks a lot

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There can be two possible points, symmetrical to the side already known. –  JiminP Nov 8 '13 at 16:09

Say you know the coordinates of the points $A$ and $B$. Then $C$ must lie on the circle centred at $A$ with radius $AC$. Simultaneously, it must lie on the circle centred at $B$ with radius $BC$.
You can express each of these two facts as a quadratic equation in the variables being the coordinates of $C$. If the coordinates of $A$ and $B$ and all the side lengths are compatible, this set will have exactly two solutions. Those will be the two possible locations of $C$.