To determine angle 𝜃, we can use the Law of Cosines formula:
c^2 = a^2 + b^2 - 2ab*cos(𝜃)
Substitute the given values of a, b, and c:
42.25^2 = 61.01^2 + 36.96^2 - 2(61.01)(36.96)*cos(𝜃)
1790.5625 = 3722.0601 + 1365.8016 - 4521.2192*cos(𝜃)
1790.5625 = 5087.8617 - 4521.2192*cos(𝜃)
-3297.2992 = -4521.2192*cos(𝜃)
Divide by -4521.2192:
cos(𝜃) = -3297.2992 / -4521.2192
cos(𝜃) ≈ 0.7286
Now, to find 𝜃, take the inverse cosine of 0.7286:
𝜃 ≈ cos^(-1)(0.7286)
𝜃 ≈ 43.25 degrees
Therefore, angle 𝜃 is approximately 43.25 degrees.
Use the Law of Cosines to determine the indicated angle 𝜃. (Assume a = 61.01, b = 36.96, and c = 42.25. Round your answer to two decimal places.)
𝜃 B=
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