Jinsi ya kukokotoa Law of Cosines
Law of Cosines ni nini?
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.
Mwongozo wa Hatua kwa Hatua
- 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
Mifano Iliyotatuliwa
Ingizo
a=8, b=11, C=37°
Matokeo
c ≈ 6.67
c²=64+121−2(8)(11)cos(37°)
Ingizo
a=5, b=7, c=10
Matokeo
C ≈ 111.8°
cos(C)=(25+49−100)/70=−0.37
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