Solve any triangle
Choose the three values you know (three sides, two sides and an angle, two angles and a side) and get every remaining side and angle, with area, perimeter, heights, steps and a scale drawing.
Side a faces vertex A, where angle α sits, and the same goes for b with β and for c with γ. Lengths carry no unit, so you can work in centimetres, metres or inches as long as all three use the same one. Angles accept decimal degrees (37.5) or degrees, minutes and seconds (37° 30' 15").
How to use it
Pick at the top which three values you know and fill in the three fields that appear. The answer updates as you type, with nothing to press. Decimals accept a dot or a comma; angles accept decimal degrees (37.5) or degrees, minutes and seconds, written as 37° 30' 15" or simply 37 30 15. Lengths carry no unit, so if you enter centimetres you read centimetres back and the area comes out in square centimetres. Switching from one case to another keeps the values you had typed, so you can compare two readings of the same problem.
Why three values are enough (and why three angles are not)
A triangle has six elements, three sides and three angles, and three of them pin it down as long as at least one is a side. That gives exactly five cases, the ones in the menu: SSS, SAS, ASA, AAS, SSA. The AAA case is missing on purpose: three angles give you the shape but not the size, because all similar triangles share the same angles with different sides. On this page vertex A carries angle α and faces side a, and the same rule holds for B with β and b, and for C with γ and c.
The formulas behind the answer
The law of cosines, a² = b² + c² - 2·b·c·cos α, handles the case where the known angle sits between the two sides (SAS) and, rearranged as cos α = (b² + c² - a²) / (2·b·c), the case of three known sides (SSS). The law of sines, a / sin α = b / sin β = c / sin γ, handles two angles and a side (ASA and AAS) once the third angle comes from α + β + γ = 180°. The area comes from Heron's formula with the semiperimeter, the inradius is r = Area / p, the circumradius is R = a·b·c / (4·Area) and each height is twice the area divided by the side it falls on. The step by step block repeats every formula with your own numbers already substituted, so you can copy it onto paper and check it.
The ambiguous SSA case, the one that costs marks
When you know two sides and an angle that is NOT between them, there can be two triangles. Picture side b resting on vertex A at inclination α, then swing side a like a compass until it reaches the base: if a is shorter than the height b · sin α it never reaches and no triangle exists; if it equals the height it touches at one point and angle β is 90°; if it lies between the height and b it touches at two points and there are two triangles, one with β acute and one with β obtuse; if it is at least as long as b the second point falls on the wrong side and you are back to a single triangle. The tool always tells you which of these situations you are in and, when there are two solutions, it shows both with their own drawing so you can pick the one matching the figure in front of you.
Stated limits and rounding
Values are shown with four decimals while the calculation runs in double precision with about fifteen digits, so an angle reading 59.9999° instead of 60° is rounding at work, not a flaw in the method. Fields accept up to 12 integer digits and 10 decimals and report an error instead of computing silently; if two angles add up to almost 180° the sides grow enormous and the tool says so rather than printing meaningless numbers. The drawing is to scale and is there to make the figure clear, not as a technical drawing: before a real cut always check with a measurement on the piece. Everything runs in your browser and no data is sent to a server.