Question

Solve the triangle. Round your answers to the nearest tenth.

Answer 1

Answer:

  B.  m∠B = 118°, a = 17, c = 18

Step-by-step explanation:

The answer choices all agree on the values of ∠B and c, so we only need to compute the value of side a.

We can verify angle B is ...

  ∠B = 180° -30° -32° = 118°

By the law of sines, ...

  a/sin(A) = b/sin(B)

Multiplying by sin(A), we get ...

  a = b·sin(A)/sin(B) = 30·sin(30°)/sin(118°) ≈ 16.98855

  a ≈ 17.0 . . . units . . . . . matches choice B

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If you like, you can also verify side c:

  c = b·sin(C)/sin(B) = 30·sin(32°)/sin(118°) ≈ 18.00512

  c ≈ 18.0 . . . units