Law of Cosines We use law of Cosines to find the length of a missing side or degree of a missing angle in an Oblique triangle(No Right Angle) In order to do this we must have some information and there are 4 conditions that will work, however only 2 use the law of Cosines, so we will focus on those today. A B C a b c In order to use law of Cosines you must know: 1.) all 3 sides 2.) 2 sides and the included angle The three angles are A, B, and C with the side opposite the angles being a, b, and c. Using Logic for rule 1: as long as we know all three sides a, b, and c. Using Logic for rule 2: If we know sides a and b and angle C. If we know sides a and c and angle B. If we know sides b and c and angle A.

a2 = b2 + c2 – 2bcCosA b2 = a2 + c2 – 2acCosB c2 = b2 + a2 – 2baCosC Law of Cosines Law of Cosines: when you know 3 sides. Law of Cosines: When you know 2 sides and the included angle. a2 = b2 + c2 – 2bcCosA b2 = a2 + c2 – 2acCosB c2 = b2 + a2 – 2baCosC These are the same equations they have just been solved for different parts.

B 11 8 C A 5 Cos A = (112 + 52 – 82)/(2(11)(5)) Cos A = A = cos-1 ( Cos B = (112 + 82 – 52)/(2(11)(8)) Cos B = B = cos-1 ( B = A 5 C = 180 - A – B C =

C #15 9 6 A B 4

C 2 45º A B 4 b2 = 42 + 22 -2(4)(2)cos 45º b = √ b = Cos A = (42 + 2 – 22)/(2(4)() A = cos-1 ( A = C = 180 – 45 – C =

#10 C 3 30º A B 4

Assignment #9 Pg. 535 (9-16)