Question

Solve the following triangle using either the law of sines or the law of cosines b=6 , c=12, A=48°

Answer 1

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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°).