Answer: approximately 95 degrees
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Work Shown:
Law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
156.5^2 = 139.5^2 + 59.5^2 - 2*139.5*59.5*cos(C)
24492.25 = 19460.25 + 3540.25 - 16600.5*cos(C)
24492.25 = 23000.5 - 16600.5*cos(C)
24492.25 - 23000.5 = -16600.5*cos(C)
1491.75 = -16600.5*cos(C)
-16600.5*cos(C) = 1491.75
cos(C) = (1491.75)/(-16600.5)
cos(C) = -0.0898617511520737
C = arccos(-0.0898617511520737)
C = 95.1556537886261
C = 95 degrees approximately
Make sure your calculator is in degree mode.
"arccos" is short for "arccosine" which is the same as inverse cosine. Your calculator may show this as the button labeled [tex]\cos^{-1}[/tex]
