Question

Use the Law of Cosines to determine the indicated angle 0. (Assume a - 139.5, b = 59.5, and c = 156.5. Round your answer to the nearest degree.)

Answer 1

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
`\cos^(-1)`