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The Law of Cosines relates the three sides of any triangle to one of its angles. It generalises the Pythagorean theorem: when the angle C = 90°, cos(C) = 0 and the formula reduces to a² + b² = c².
Trinn-for-trinn guide
- 1Label the triangle sides a, b, c and opposite angles A, B, C
- 2To find side c: c² = a² + b² − 2ab·cos(C)
- 3To find angle C: cos(C) = (a² + b² − c²) / 2ab
Løste eksempler
Inndata
a=8, b=11, C=37°
Resultat
c ≈ 6.67
c²=64+121−2(8)(11)cos(37°)
Inndata
a=5, b=7, c=10
Resultat
C ≈ 111.8°
cos(C)=(25+49−100)/70=−0.37
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