Solve for a triangle's sides, angles, area, and more, from three known sides or angles.
A triangle is fully determined by any three of its six measurements (three sides, three angles), as long as at least one side is included — three angles alone only fix the triangle's shape, not its size. SSS (three sides), SAS (two sides and the angle between them), and ASA (two angles and the side between them) are the three most common starting points.
The law of cosines (a²=b²+c²-2bc·cos A) generalizes the Pythagorean theorem to any triangle, and is what makes solving SSS and SAS possible. The law of sines (a/sin A = b/sin B = c/sin C) relates sides to their opposite angles, and is what makes solving ASA possible.
The inradius is the radius of the largest circle that fits entirely inside the triangle, touching all three sides. The circumradius is the radius of the circle that passes through all three vertices. Every triangle has exactly one of each.
The triangle inequality requires that the sum of any two sides be greater than the third — if that's violated (say, sides 2, 3, and 10), no triangle exists with those measurements.
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