Use the Law of Cosines to determine the indicated angle 𝜃. (Assume a = 130.5, b = 60.1, and c = 162.5. Round your answer to the nearest degree.)
𝜃 =
find angle C
To find angle C using the Law of Cosines, we can use the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given values:
162.5^2 = 130.5^2 + 60.1^2 - 2 * 130.5 * 60.1 * cos(C)
26406.25 = 17030.25 + 3612.01 - 15621.9 * cos(C)
26406.25 = 20642.26 - 15621.9 * cos(C)
5773.99 = - 15621.9 * cos(C)
cos(C) = -5773.99 / 15621.9
cos(C) = -0.369677
Now, to find angle C, we take the arccos of -0.369677:
C = arccos(-0.369677)
C ≈ 110.7 degrees
Therefore, the indicated angle 𝜃 is approximately 110 degrees.