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Ambiguous Law of Sines. Remember SSA?. Compute b sin A, then compare to a. No solution. One Solution. Two Solutions. One Solution. Compute side a to side b. One Solution. No solution. Example 1. No solutions. One Solution. Two solutions. Compute side a to side b. One Solution.
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Ambiguous Law of Sines Remember SSA? Compute b sin A, then compare to a No solution One Solution Two Solutions One Solution Compute side a to side b One Solution No solution
Example 1 No solutions One Solution Two solutions Compute side a to side b One Solution No solution Compute b sin A, then compare to a No solution Case 1: A < 90 & a < b One Solution Which is true? Two Solutions Compare a to b sinA: One Solution Calculate b sinA Case 2: B > 90 Which is true? Compare b to c: No solutions One Solution
Example 2 Draw a picture:
Compute c sin A, then compare to a No solution One Solution Two Solutions One Solution We noted at the beginning that there should be two possible solutions. Since one solution for Angle C = 76.3, the other possibility is 180 – 76.3 = 103.7
