Calculatrice de la Loi des Cosinus Gratuite
Résolvez des triangles avec la loi des cosinus. Trouvez un côté ou un angle manquant quand vous connaissez les trois autres.
Side C
8.8882
Formule
Law of Cosines
Formula
c² = a² + b² - 2ab × cos(C)
c = sqrt(a² + b² - 2ab × cos(C))
This generalizes the Pythagorean theorem. When C = 90°, cos(C) = 0, and it reduces to c² = a² + b².
When to Use
Exemple Résolu
Find side c: a = 7, b = 10, angle C = 60°.
- 01c² = 49 + 100 - 2(7)(10)cos(60°)
- 02= 149 - 140 × 0.5
- 03= 149 - 70 = 79
- 04c = √79 ≈ 8.8882
Questions Fréquentes
What is the law of cosines?
The law of cosines relates the three sides of a triangle to one of its angles: c² = a² + b² - 2ab cos(C). It generalizes the Pythagorean theorem.
How is this related to the Pythagorean theorem?
When angle C is 90°, cos(90°) = 0, so the formula becomes c² = a² + b², which is the Pythagorean theorem. The law of cosines works for all triangles, not just right triangles.
Can I find an angle using the law of cosines?
Yes, rearrange to: cos(C) = (a² + b² - c²) / (2ab). Then take the arccos to find the angle.
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