Unlock the power of the Law of Cosines with our easy-to-use Cosine Triangle Calculator. Whether you have two sides and an included angle (SAS) or all three sides (SSS), this tool quickly determines unknown sides, angles, and even the area of your triangle. Solve complex geometry problems with precision and ease.
Formula:
The Law of Cosines is a fundamental theorem relating the lengths of the sides of a triangle to the cosine of one of its angles. It extends the Pythagorean theorem to non-right triangles.
- To find a side (SAS - Side-Angle-Side):
a² = b² + c² - 2bc cos(α)b² = a² + c² - 2ac cos(β)c² = a² + b² - 2ab cos(γ)- Where:
a, b, care the lengths of the triangle's sides.α(alpha) is the angle opposite sidea.β(beta) is the angle opposite sideb.γ(gamma) is the angle opposite sidec.- To find an angle (SSS - Side-Side-Side):
cos(α) = (b² + c² - a²) / (2bc)cos(β) = (a² + c² - b²) / (2ac)cos(γ) = (a² + b² - c²) / (2ab)