Use the Law of Cosines to determine the indicated angle ๐. (Assume a = 61.01, b = 36.96, and c = 42.25. Round your answer to two decimal places.)
๐ B=
To determine angle ๐, we can use the Law of Cosines formula:
c^2 = a^2 + b^2 - 2ab*cos(๐)
Substitute the given values of a, b, and c:
42.25^2 = 61.01^2 + 36.96^2 - 2(61.01)(36.96)*cos(๐)
1790.5625 = 3722.0601 + 1365.8016 - 4521.2192*cos(๐)
1790.5625 = 5087.8617 - 4521.2192*cos(๐)
-3297.2992 = -4521.2192*cos(๐)
Divide by -4521.2192:
cos(๐) = -3297.2992 / -4521.2192
cos(๐) โ 0.7286
Now, to find ๐, take the inverse cosine of 0.7286:
๐ โ cos^(-1)(0.7286)
๐ โ 43.25 degrees
Therefore, angle ๐ is approximately 43.25 degrees.