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tigry1 [53]
2 years ago
10

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

Mathematics
2 answers:
8090 [49]2 years ago
6 0

Answer:

b = 29.0, A = 123.9°, C = 20.1°

andre [41]2 years ago
5 0

9514 1404 393

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

__

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°

_____

<em>Additional comment</em>

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°.

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