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With the distance formula.

Call the points A, B, and C. Call the sides ab, bc, and ca.

If we know where points A and B are, we can figure out the location of point C.

We use two distance formulas. The length of cb and the location of B will give us a set of points an equal distance from point B (a circle with center at B). The length of ca and the location of A will give us a set of points an equal distance from point A (a circle with center at A).

The intersection of these two sets (set the distance formulas equal to each other, or otherwise solve for the solution of a set of equations) will be the two possibilities of the vertex C.

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