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Explanation & Answer
Use Law of Cosines
c2 = a2 + b2 - 2abcosC
13^2 = 11^2 + 12^2 - 2(11)(12)cosC
169 = 121+144 - 264cosC
169 = 265 - 264cosC
264cosC = 96
cosC = 96/264 = 0.3636
C = arccos(0.3636) = 68.68 degrees
Now use Law of Sines to get the other angles
13/sin68.68 = 11/sinA
sinA = 11sin68.68/13 = 0.788
A = arcsin(0.788) = 52.02 degrees
11/sin52.02 = 12/sinB
sinB = 12sin52.02/11 = 0.86
B = arcsin(0.86) = 59.3 degrees
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