Answer:
- b = 47.6
- A = 50.1°
- C = 55.9°
Step-by-step 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°
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Additional comment
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