Kako izračunati Law of Cosines
Što je Law of Cosines?
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.
Vodič korak po korak
- 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
Worked Examples
Unos
a=8, b=11, C=37°
Rezultat
c ≈ 6.67
c²=64+121−2(8)(11)cos(37°)
Unos
a=5, b=7, c=10
Rezultat
C ≈ 111.8°
cos(C)=(25+49−100)/70=−0.37
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