9514 1404 393
Answer:
(a, B, C) ≈ (9.15, 29.2°, 102.8°)
Step-by-step explanation:
The given angle lies between the given sides, so the law of sines cannot be used. The third side is ...
a² = b² +c² -2bc·cos(A) ≈ 83.6452
a ≈ √83.6452 ≈ 9.146
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Then angle B is found from the law of sines. We want to find the smaller angle, so we can tell if the triangle is acute or obtuse.
sin(B)/b = sin(A)/a
B = arcsin(b/a·sin(A)) ≈ arcsin(0.48753)
B ≈ 29.2°
C = 180° -48° -29.2° = 102.8°
The solution to the triangle is (a, B, C) = (9.1, 29.2°, 102.8°).
