Triangle Solver (Two Angles and the Included Side)

a measured baseline and the two angles to a point you cannot reach directly. C = 180 - A - B, then the law of sines a = c sin A/sin C and b = c sin B/sin C give the distances to the far point. Sight a target at 70.89 and 49.11 degrees off a 9.165 ft baseline and it is 10.0 and 8.0 ft from the two ends - the same 10-8-9.165 triangle the SAS and SSS solvers build, so all three agree. That is how a surveyor or layout hand reaches a distance to an inaccessible corner, tower, or bank with no tape to the point. The two angles must sum to under 180 degrees. Ambiguous SSA is separate. A layout aid; verify critical dimensions on the work.

C = 180 - A - B; a = c sin(A)/sin(C); b = c sin(B)/sin(C); area = (1/2) a b sin(C). A + B < 180 required.

The law of sines a/sin(A) = c/sin(C) with C = 180 - A - B - first-principles plane trigonometry as in Machinery's Handbook (Industrial Press), by name; public domain.

Pure plane trigonometry, public; the two angles and the baseline are user-supplied measurements.

Estimate. AHJ and licensed professional govern.

Field names used by the API: angle_a_deg, angle_b_deg, included_side_c, angle_c_deg, side_a, side_b

• Law of sines C = 180 - A - B, then a = c sin A/sin C, b = c sin B/sin Cplane trigonometry
• Angle sum A + B must be under 180 degrees (the sight lines must meet)geometry