Algebra & Trig, Sullivan & Sullivan
Fourth Edition
Notes:§8.3
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§8.3 – Law Of Cosines
c 2  a 2  b 2  2  a  b  cos 
(and similarly,
2
2
a  c  b 2  2  c  b  cos 
Law Of Cosines
b 2  c 2  a 2  2  c  a  cos 
Law Of Cosines: Case 3 (2 sides, 1 angle between them)
SAS
<Notice that we can't use the law of sines here, since we don't have any angles opposite sides
(thus, no ratios), nor do we have enough info to get the remaining angles>
(If the problem is given in degrees, make sure that your calculator is in degrees mode!)
Law Of Cosines: Case 3 (3 sides)
SSS
Pick one of the Law of Cosines equations, isolate the cos(X) term. Then use the cos-1 (arcos)
to figure out what the angle must be.