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Precalc 5.5: Solving an Oblique Triangle using Law of Sines, The Ambiguous Case – A Pain in the SSA Given two consecutive sides and a non-included angle [SSA], ZERO, ONE or TWO TRIANGLES may exist For example, given sides a and b, and angle A, first: use Law of Sines to find If , then no triangles exist and you are done If , then at least one triangle exists. Find angle B1, using then find angle B2: If , only one triangle exists. Solve it using Law of Sines and Rule of 180 If , , two triangles exist. Solve them both using Law of Sines and Rule of 180. Note: The given Angle and sides will be the same for both triangles. The non-given angles and side will have different values.
