🔺 Triangle Solver

SSS · SAS · law of cosines · Heron area · inequality checked

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A triangle is fully determined by three sides (SSS) or two sides and the angle between them (SAS) — this solver takes either, uses the law of cosines for the angles (never the law of sines, whose ambiguous case silently produces two answers), and Heron's formula for the area. If the sides cannot close into a triangle, the page says so and shows which inequality failed.

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The ambiguous case the law of sines walks into

Given two sides and a non-included angle, sin⁻¹ returns two angles (θ and 180−θ) and both can be geometrically legal — the SSA "ambiguous case" that school trigonometry quietly warns about. The law of cosines avoids the trap entirely because acos returns exactly one value in 0–180°, which is why every angle on this page is computed with it. Heron's formula closes the loop: area from sides alone, no height measurement needed — surveyors have used the pair of tricks to triangulate fields since before calculators existed.

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