Kosinussatz-Rechner — Formel

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

  • You know two sides and the included angle (SAS) and want the third side
  • You know all three sides (SSS) and want an angle

    • Lösungsbeispiel

    Find side c: a = 7, b = 10, angle C = 60°.

    1. c² = 49 + 100 - 2(7)(10)cos(60°)
    2. = 149 - 140 × 0.5
    3. = 149 - 70 = 79
    4. c = √79 ≈ 8.8882