Question

Triangle ABC has side lengths a= 24, b= 40, and c= 55. What is the measure of angle C? 83.6° 116.2° 23.0° 40.7°

Answer 1

Answer: 116.2°

Work Shown:

`c^2 = a^2 + b^2 - 2ab\cos(C)\\\\55^2 = 24^2 + 40^2 - 2*24*40\cos(C)\\\\3025 = 576 + 1600 - 1920\cos(C)\\\\3025 = 2176 - 1920\cos(C)\\\\3025 - 2176 = -1920\cos(C)\\\\849 = -1920\cos(C)\\\\-1920\cos(C) = 849\\\\\cos(C) = (849)/(-1920)\\\\\cos(C) \approx -0.4421875\\\\C \approx \cos^(-1)(-0.4421875)\\\\C \approx 116.243535748231^(\circ)\\\\C \approx 116.2^(\circ)\\\\`

The first equation is one of the three variations for the Law of Cosines.

Make sure your calculator is in degree mode.