Answer:
b. b = 15.0, A = 113.2°, C = 300°
Step-by-step explanation:
The given sides are either side of the given angle, so the Law of Cosines can be used to find the unknown side.
b² = a² +c² -2ac·cos(B)
b² = 23² +12.5² -2(23)(12.5)cos(36.8°) = 224.829
b = √224.829 = 14.99 ≈ 15.0 . . . . . matches choice B
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For the purpose of selecting the correct multiple-choice answer, this is sufficient working.
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If you want to find the remaining angles, you can use the law of sines to find one of them. The smallest angle* will be ...
sin(C)/c = sin(B)/b
C = arcsin(c/b·sin(B)) = arcsin(12.5/14.9942·sin(36.8°)) ≈ 30.0°
Then angle A can be found from the sum of angles in a triangle:
A = 180° -36.8° -30° = 113.2° . . . . . also matches choice B
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* We choose to find the smallest angle because the largest one may be more than 90°. The Law of Sines is ambiguous in that case. Finding the smaller angle first resolves the ambiguity immediately.
