The Ambiguous Case (SSA)

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The Ambiguous Case (SSA) 20. Law of Sines The Ambiguous Case (SSA)

The Ambiguous Case (SSA) Yesterday we saw that two angles and one side determine a unique triangle. However, if two sides and one opposite angle are given, three possible situations can occur: (1) no triangle exists, (2) one triangle exists, or (3) two distinct triangles may satisfy the conditions.

Flowchart for ambiguous case

Steps for ambiguous case Set up law of sines and solve for sin of missing angle Use the flow chart

Example In triangle ABC, b = 2, c = 8, and B = 120°. Solve the triangle. C B A? a 2 8 120°

Example In triangle ABC, c = 10, a = 6, and A = 28°. Solve the triangle.

Example In triangle ABC, a = 6.5, b = 7.4, and B = 79°. Solve the triangle.