Answer:
B. 129.7°
Step-by-step explanation:
The law of sines tells you ...
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin((c/a)sin(A)) = arcsin(117/57·sin(22°)) = 50.3°
The value shown is the result of using the arcsin function, but we know that the supplement of this angle has the same sine value. Then, we could have ...
C = 180° -50.3° = 129.7°
The figure shows C as an obtuse angle, so we choose this latter value as the appropriate answer to this question.
C = 129.7° . . . . . matches choice B
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Comment on the answer
We note that choice C (50.3°) matches the result of straightforward use of the law of sines. This triangle actually has two solutions for angle C, as we have noted above. Often, figures are "not to scale," so the appearance of angle C as an obtuse angle cannot always be taken at face value. Here, because both choices for angle C are offered, we use the appearance of the figure to help decide the right one.
