Triangle Solver (Three Sides)

Three measured sides, find the angles - how you check whether a corner is square from a tape (the 3-4-5), read the angle of a brace or lot line from three lengths, or area a triangular patch. Each angle is the law of cosines A = acos((b^2 + c^2 - a^2)/(2bc)); the area is Heron's sqrt(s(s-a)(s-b)(s-c)). Sides 10, 8, 9.165 open 70.9, 49.1, 60.0 degrees (the same triangle the two-sides-and-included-angle solver builds from 10 and 8 at 60), and 3, 4, 5 gives exactly 90 degrees opposite the 5 - the framer square-corner check, generalized. The three sides must satisfy the triangle inequality or no triangle exists. SAS is its own solver; ASA/AAS and ambiguous SSA are separate. A layout aid; verify critical dimensions on the work.

A = acos((b^2 + c^2 - a^2)/(2bc)) and likewise B, C; s = (a+b+c)/2; area = sqrt(s(s-a)(s-b)(s-c)) (Heron). Triangle inequality required.

The law of cosines solved for the angles with Heron's area formula - first-principles plane trigonometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure plane trigonometry, public; the three sides are user-supplied measurements.

Estimate. AHJ and licensed professional govern.

Field names used by the API: side_a, side_b, side_c, angle_a_deg, angle_c_deg, area

• Law of cosines + Heron angles from acos((b^2+c^2-a^2)/(2bc)); area = sqrt(s(s-a)(s-b)(s-c))plane trigonometry
• Triangle inequality each side must be less than the sum of the other twogeometry