Triangle Solver: SSS, SAS, ASA, AAS & SSA

Give any three independent facts about a triangle and the rest follows. This solver takes the five cases that fix a triangle — three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), two angles and a side opposite one of them (AAS), or two sides and an angle opposite one of them (SSA) — and returns every side and angle, the area, perimeter, inscribed and circumscribed radii, the three heights and the three medians, whether the triangle is acute, right or obtuse and whether it is equilateral, isosceles or scalene, with a drawing to scale. Side a is always opposite angle A, and angles can be entered in degrees or radians. SSA is the ambiguous case: given a, b and the angle A opposite a, there may be two different triangles, exactly one, or none at all. When a is at least b there is one; when a is shorter, the side can swing to two positions, touch the base line at one right angle, or fall short of it, and the tool shows each triangle that exists. Three angles alone (AAA) fix only the shape, not the size, so that case is not offered. The arithmetic is chosen for thin triangles, where textbook formulas lose digits: angles come from the half-angle tangent formula rather than the arc cosine of the law of cosines, and the area from Kahan's rearrangement of Heron's formula, so a needle-shaped triangle such as 10, 10, 19.99 still gets its small angle and area to full precision. Inputs that cannot form a triangle — sides that break the triangle inequality, angles that add up to 180° or more — are refused with the reason.