Answer: 62.2 degrees
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Explanation:
The given side lengths are
Use the law of cosines to determine angle C.
[tex]c^2 = a^2 + b^2 - 2*a*b*\cos(C)\\\\8^2 = 9^2 + 5^2 - 2*9*5*\cos(C)\\\\64 = 106 - 90*\cos(C)\\\\64-106 = -90\cos(C)\\\\-42 = -90\cos(C)\\\\-90\cos(C) = -42\\\\\cos(C) = -42/(-90)\\\\\cos(C) \approx 0.4666667\\\\C \approx \cos^{-1}(0.4666667)\\\\C \approx 62.1818586^{\circ}\\\\C \approx 62.2^{\circ}[/tex]
Make sure your calculator is in degree mode.
