Law of Cosines, Law of Sines, and triangle area

MathematicsPlane GeometryAges 15–16

Triangle ABC is built from two sides a, b and the included angle C; drag any of the three vertices freely. Every side and angle updates live while you verify: c² = a² + b² − 2ab·cosC, a/sinA = b/sinB = c/sinC = 2R, and area S = ½ab·sinC = √(p(p−a)(p−b)(p−c)) = abc/4R = pr. You can also show the circumscribed circle (radius R) and the altitude.