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SSA ambiguous case

Rotate the endpoints of the 3 options for side a of this triangle to see the triangles that are possible with the given lengths. To change the lengths of side a or b slide the a_1 or b_1 slider. To change the angle move point C The length of a_0 is a critical length to determine whether one or two triangles can be formed. How can the length of a_0 be found? How is this diagram calculating it?