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Algebra 2: Unit 10: Law of Sines NAME: _____________________________ Solve the right triangles by finding all the missing parts. 1. A 2. X 12 c b 6 36 B C Y z 9 B= A= X= b= c= z= Y= Now we are going to solve triangles that have no right angles, using similar techniques. C Use when you have…. a b A B c Law of Sines… Examples: Find the remaining sides and angles. C 1. a 27 102 28 B c A E 2. f d D 96 23 30 F . The Ambiguous Case (SSA) If the given angle < 90 , then test for 4 possible cases. Case 1: No Solution Case 2: One Solution Ex: a = 15, b = 25, and A = 85 Ex: a = 4, b = 8, and A = 30 Case 3: Two Solutions Case 4: One Solution Ex: a = 12, b = 31, and A = 20.5 Ex: a = 22, b = 12, and A = 42 Case 1: No Solution Ex: a = 25, b =30 , and A = 117 If the given angle > 90 , then test for 2 possible cases. Case 2: One Solution Ex: a = 28, b = 24, and A = 125 Practice: Use the Law of Sines to solve for the missing sides and angles of the triangle (if possible). 1. B = 150 , b = 30, c = 10 2. B = 150 , a = 10, b = 3 3. A = 75 , a = 51.2, b = 33.7 4. B = 25 , a = 6.2, b = 4