Question
Triangle upper A upper B upper C has each of the interior angles by its vertices labeled with singular arcs. Side upper A upper B is labeled c, side upper A upper C is labeled b, and side upper B upper C is labeled a.
Imagine that a is 5 feet, b is 21 feet, and c is 18 feet. If angle B
is 55 degrees, find angle C
. Round your answer to the nearest degree.
(1 point)
degrees
Answers
GPT 3.5
To find angle C, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C)
Substitute the given values:
18^2 = 5^2 + 21^2 - 2*5*21*cos(55)
324 = 25 + 441 - 210*cos(55)
318 = 466 - 210*cos(55)
210*cos(55) = 148
cos(55) = 148/210
cos(55) ≈ 0.7057
Now, find angle C:
cos(C) = (a^2 + b^2 - c^2) / 2ab
cos(C) = (5^2 + 21^2 - 18^2) / (2*5*21)
cos(C) = (25 + 441 - 324) / 210
cos(C) = 142 / 210
cos(C) = 0.6762
C = arccos(0.6762)
C ≈ 47 degrees
Therefore, angle C is approximately 47 degrees.
c^2 = a^2 + b^2 - 2ab*cos(C)
Substitute the given values:
18^2 = 5^2 + 21^2 - 2*5*21*cos(55)
324 = 25 + 441 - 210*cos(55)
318 = 466 - 210*cos(55)
210*cos(55) = 148
cos(55) = 148/210
cos(55) ≈ 0.7057
Now, find angle C:
cos(C) = (a^2 + b^2 - c^2) / 2ab
cos(C) = (5^2 + 21^2 - 18^2) / (2*5*21)
cos(C) = (25 + 441 - 324) / 210
cos(C) = 142 / 210
cos(C) = 0.6762
C = arccos(0.6762)
C ≈ 47 degrees
Therefore, angle C is approximately 47 degrees.