Find all three angles of a triangle given its three side lengths.
Solve a triangle's remaining sides and angles from what you already know — three sides (SSS), or two sides and the angle between them (SAS) — using the Law of Cosines to find the missing piece, then the Law of Sines for the rest.
The Law of Cosines generalizes the Pythagorean theorem to any triangle, not just right triangles: c² = a² + b² − 2ab·cos(C). With SSS input, it's rearranged to solve for each angle directly. With SAS input, it finds the third side first, then the Law of Sines finds the remaining two angles from the sides and the one angle already known.
Not every three numbers make a valid triangle — the triangle inequality (any two sides must add up to more than the third) has to hold, and this checks for that rather than silently returning a nonsensical result.
It checks the triangle inequality (any two sides must sum to more than the third) before solving, and tells you plainly if the numbers you entered can’t form a real triangle, rather than returning a meaningless answer.
The Law of Cosines is what actually solves for a missing side or the angle opposite a known side combination — once one angle is known, the Law of Sines is a simpler way to find the remaining two from the ratio of sides to their opposite angles.
Yes — a right triangle is just a normal triangle with one 90° angle, and the same Law of Cosines calculation reduces to the Pythagorean theorem exactly when the included angle is 90°.