find the measure for each of the three angles

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Feb 3rd, 2015

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

Feb 3rd, 2015

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