5.7 The Ambiguous Case for the Law of Sines

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Presentation transcript:

5.7 The Ambiguous Case for the Law of Sines Objective: Determine whether a triangle has zero, one, or two possible configurations. Solve triangles using the Law of Sines.

Law of Sines Let ∆ABC be any triangle with a, b, and c representing the measures of sides opposite angles with measurements A, B, and C, respectively. Then

Case A ≥ 90° A = 110°, a = 10, b = 20 No solution!

Case A ≥ 90° A = 110°, a = 20, b = 10 One solution!

Case A < 90° A = 85°, a = 15, b = 25 No solution!

Case A < 90° A = 30°, a = 5, b = 10 One solution!

Case A < 90° A = 30°, a = 7, b = 10 Two solutions!

Case A < 90° A = 30°, a = 12, b = 10 One solution!

Assignment 5.7 Practice Worksheet #5-11 5.7 pg 324 #18, 20, 24, 35