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GIVING 50 POINTS!!!

Solve the triangle using the law of sines. Show all work and round answers to the nearest tenth.

GIVING 50 POINTS!!! Solve the triangle using the law of sines. Show all work and round-example-1

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Answer:

  • a = 27, ∠A = 28°, ∠B = 7°

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Use the law of sines:

  • a/sin ∠A = b/sin ∠B = c/sin ∠C

Use the given values and find the measure of angle B:

  • 7/sin ∠B = 33/sin 145°
  • sin ∠B = 7 sin 145°/33
  • sin ∠B = 0.12166
  • ∠B = arcsin (0.12166)
  • ∠B = 7° (rounded)

We have now two angle measures.

Use triangle sum theorem to find the third angle:

  • ∠A + ∠B + ∠C = 180°
  • ∠A + 7° + 145° = 180°
  • ∠A + 152° = 180°
  • ∠A = 28°

Find the last side length:

  • a/sin ∠A = b/sin ∠B
  • a/sin 28° = 7/sin 7°
  • a = 7 sin 28° / sin 7°
  • a = 27.0 (rounded)

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