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B=74° a=38 c= 41 find other sides and angles

1 Answer

9 votes

Answer:

  • b = 47.6
  • A = 50.1°
  • C = 55.9°

Explanation:

The Law of Cosines is used to solve triangles in which two sides and the included angle are given. It tells you ...

b² = a² +c² -2ac·cos(B)

Filling in the given values, we find ...

b² = 38² +41² -2·38·41·cos(74°)

b² ≈ 2266.114

b ≈ √2266.114 ≈ 47.604

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Once the three sides and an angle are known, another angle can be found using the Law of Sines.

sin(A)/a = sin(B)/b

A = arcsin(a/b·sin(B)) ≈ arcsin(38/47.604·sin(74°)) ≈ arcsin(0.767334)

A ≈ 50.1°

C ≈ 180° -74° -50.1° = 55.9°

The other sides and angles are ...

  • b = 47.6
  • A = 50.1°
  • C = 55.9°

_____

Additional comment

Triangle solver apps are available on many platforms: phone, tablet, web browser. Your calculator may have one.

B=74° a=38 c= 41 find other sides and angles-example-1
User Kelp
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