Question

Solve the triangle. B = 36°, a = 41, c = 17 (5 points)

Answer 1

Answer:

b = 29.0, A = 123.9°, C = 20.1°

Answer 2

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Answer:

  b = 29.0; A = 123.9°, C = 20.1°

Step-by-step explanation:

The given angle lies between the given sides, so the Law of Cosines is the appropriate relation.

  b² = a² +c² -2ac·cos(B)

  b² = 1681 +289 -1394cos(36°) ≈ 842.2303

  b ≈ √842.2303 ≈ 29.021

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The Law of Sines can be used to find angle C:

  sin(C)/c = sin(B)/b

  C = arcsin(c/b·sin(B)) = arcsin(17/29.021×sin(36°))

  C ≈ 20.1°

  A = 180° -36° -20.1° = 123.9°

The remaining side and angles are ...

  b ≈ 29.0; A ≈ 129.9°; C ≈ 20.1°

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Additional comment

By choosing to find the smaller angle C first, we avoid having to deal with the ambiguity associated with the arcsine when the angle is greater than 90°.