9.1 Law of Sines

Law of Sines Used to solve oblique s ( s that are NOT right s) OR

Case 1: 2 Angles & 1 side known(AAS or ASA) Case 1: 2 Angles & 1 side known(AAS or ASA) Ex 1) Solve the triangle where A = 37 , B = 82 , and a = 23 B C = 180 - 37 - 82 = 61 82 c a = 23 A 37 C b

Case 1: 2 Angles & 1 side known Ex 1) Solve the triangle where Case 1: 2 Angles & 1 side known Ex 1) Solve the triangle where A = 37 , B = 82 , and a = 23 B 82 c a = 23 A 37 C b a = 23 A = 37 b = 38 B = 82 c = 33 C = 61 answer when “solving” a

Case 2: 2 sides & 1 angle opposite one of those sides known (Ambiguous) (ASS – can’t do but know case 2) Case 2: 2 sides & 1 angle opposite one of those sides known A known angle is obtuse if a  b, then no if a > b, then unique A known angle is acute sinB > 1 → no sinB = 1 → right 0 < sinB < 1 → either 1 or 2 s or 0 < sinB < 1

Ex 2) Solve the triangle where A = 123 , a = 14, b = 21 Obtuse Impossible!!! → No (Ambiguous Case with no solution)

Ex 3) Solve the triangle where A = 48 , a = 61, b = 32 Acute Ex 3) Solve the triangle where A = 48 , a = 61, b = 32 Sine is (+)  B in QI or QII B = sin-1(0.3898) = 23° Or B = 180° - 23° = 157° But if B = 157° and A = 48° Not possible since 157 + 48 > 180 So, B = 23° C = 180° - 48° - 23° = 109°

Ex 3) Solve the triangle where A = 48 , a = 61, b = 32 b = 32 B = 23° c = 78 C = 109° (Ambiguous Case w/ unique solution)

Homework #901 Pg. 553 1 – 12 all