9514 1404 393
Answer:
a = 94.8, B = 29.3°, C = 31.7°
Explanation:
Side 'a' can be found using the Law of Cosines:
a² = b² +c² -2bc·cos(A)
a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8
Then one of the other angles can be found from the Law of Sines.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°
Then the remaining angle can be found to be ...
B = 180° -A -C = 180° -119° -31.7° = 29.3°
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The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.