Triangle Solver with Sine and Cosine Rules

How to calculate

Use the cosine rule for an included angle or for SSS angles. For ASA, first find the third angle from the angle sum, then apply the sine rule. Convert all sides to a common length unit before solving.

a²=b²+c²−2bc cos A; a/sin A=b/sin B=c/sin C; A+B+C=180°; area=½bc sin A

Worked example

Sides a=3 m, b=4 m and c=5 m give A≈36.8698976°, B≈53.1301024° and C=90°, with area 6 m² and perimeter 12 m. With A=B=60° and c=5 m, the ASA solution is an equilateral triangle with all sides 5 m.

Assumptions and input details

Side a is opposite angle A, and similarly for b/B and c/C. SAS uses angle A between sides b and c. ASA uses the side c between vertices A and B. Only these unique-solution modes are supported; the ambiguous SSA case is intentionally excluded. Known and solved sides must be 1e−12–1e9 m. Strict triangle inequalities and positive angles are required; very flat triangles near floating-point resolution are rejected. Angle changes reinterpret the entered numeric values in the selected unit. The drawing uses equal axis scales but is not at physical scale.