Triangle solver
Three known values solve the triangle — this page does the law of sines and cosines for you. Give it any valid combination (two sides and an angle, three sides, two angles and a side) and it returns every side, every angle, and the area. It flags the ambiguous SSA case where two triangles fit the data, instead of silently picking one.
The everyday uses: taper angles from measured offsets, dovetail widths over pins, chamfer edge breaks, and any layout where the print gives you one description of a corner and inspection needs another.
Enter exactly two values; at least one must be a side.
Convention: side a is opposite angle A, side b is opposite B, and side c is opposite C.
Enter exactly two known values for the right triangle, with at least one side.
Right triangles use c^2 = a^2 + b^2 and trig ratios; oblique triangles use law of sines/cosines and area = 1/2ab sin C.
Circular layout geometry: Chord, arc & radius.
When do machinists solve a triangle?
Any three known parts of a triangle — as long as one is a side — determine one or more candidate solutions, and the law of sines and cosines return them. On the shop floor that comes up constantly: a taper angle from measured offsets, a dovetail width over pins, a chamfer edge break, or converting a corner the print describes one way and inspection needs another.
Enter any valid combination (SSS, SAS, ASA, or SSA) and the solver returns every side, every angle, and the area. The SSA case can fit two different triangles; the solver returns both rather than silently choosing one, so you decide which matches the part in front of you.