Triangle Solver – Law of Sines & Cosines
Triangle Solver: Law of Sines & Cosines a/sin A = b/sin B = c/sin C = 2R
Choose the given data and enter the sides and angles (angles in degrees; 47°30' is accepted). The tool finds all three sides, all three angles in degrees and minutes, the area S, the radii R and r, the three altitudes, and draws the triangle to scale.
The solver above finds the missing sides and angles of a triangle, then computes the area, circumradius R, inradius r, and heights.
Formulas used
a/sin A = b/sin B = c/sin C = 2R
a² = b² + c² − 2bc·cos A
S = ½·bc·sin A, r = S/p
- p is the semi-perimeter (a + b + c)/2.
- The sum of the angles is always 180°.
Worked example
b = 5, c = 8, A = 60°:
a² = 25 + 64 − 40 = 49 ⇒ a = 7
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Enter three known elements (SSS, SAS, ASA, or AAS).
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.