Answer:
1. c = 28.1, A = 19°, C = 144°
2. c = 2.0, A = 161°, C = 2°
Step-by-step explanation:
In general, if the given angle is not opposite the longest side, there will be two solutions. That is the case here.
Angle A can be found from the law of sines. It will be ...
A = arcsin(a/b·sin(b)) = arcsin(15.73/13.8·sin(17°)) ≈ arcsin(0.333261) ≈ 19.46°
or the supplement of that, 160.54°.
Angle C will be the angle required to make the sum of angles be 180°, either 143.53° or 2.47°.
Side c will be ...
c = b·sin(C)/sin(B) ≈ 47.2002×sin(C)
either 28.053 or 2.032.
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There are two possible triangles:
(A, C, c) = (19°, 144°, 28.1) or (161°, 2°, 2.0)
