Triangle with vertices A, B, C and sides a (BC), b (AC), c (AB)
This comprehensive triangle solver uses both the Law of Sines and Law of Cosines to solve all possible triangle cases. Whether you know three sides (SSS), two sides and an angle (SAS, SSA), or two angles and a side (ASA, AAS), this calculator provides step-by-step solutions with clear explanations.
Triangle with vertices A, B, C and sides a (BC), b (AC), c (AB)
\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} = 2R\)
Used for: ASA, AAS, SSA (ambiguous case)
\(a^2 = b^2 + c^2 - 2bc\cos(A)\)
\(b^2 = a^2 + c^2 - 2ac\cos(B)\)
\(c^2 = a^2 + b^2 - 2ab\cos(C)\)
Used for: SSS, SAS
How to use: Select your triangle case from the dropdown below, enter the known values (angles in degrees), and click "Solve Triangle". The calculator will show you every step, from formula application to final result, with proper handling of the ambiguous SSA case.
Solve triangle when all three sides are known
Solve triangle when two sides and their included angle are known
* Angle A is the angle between sides b and c
Solve triangle when two sides and a non-included angle are known (0, 1, or 2 solutions)
* Side a is opposite angle A, side b is adjacent to angle A
Solve triangle when two angles and the included side are known
Solve triangle when two angles and a non-included side are known
* Side a is opposite angle A