Solve triangles from any combination of sides and angles. Shows the triangle to scale with all computed values and area.
Give the tool any three facts that pin down a triangle - three sides, two sides and their included angle, two angles and one side - and it computes the missing sides and angles, the area, and redraws the triangle to scale with every value labeled on it. Which formula runs depends on what you supplied: the law of cosines handles the side-heavy cases, the law of sines the angle-heavy ones. The surprise most people hit: side-side-angle input is genuinely ambiguous. Some number triples fit zero, one, or two different triangles, and a single-number answer can hide the second one.
A concrete input and expected output from the current implementation.
Input
angles A = 50 deg and B = 60 deg, plus the side between them, c = 10
Expected output
C = 70 deg, a = 8.15, b = 9.22, area = 35.3 square units
Angles must total 180 deg, so C = 180 - 50 - 60 = 70 deg. The law of sines scales the known side: a = 10 x sin(50)/sin(70) = 8.15 and b = 10 x sin(60)/sin(70) = 9.22, and the area is 0.5 x a x b x sin(70) = 35.3.
Your three inputs are classified into a textbook case: SSS, SAS, ASA/AAS, or SSA. The law of cosines is applied first for cases that begin with sides, the law of sines for cases that begin with an angle opposite a known side, and the angle-sum rule (angles total 180 degrees) supplies the third angle. Area is one half of two sides times the sine of the included angle.
The first known side becomes the base, the third vertex is placed from the computed angles or lengths, and the figure is drawn to scale so the shape is right at a glance. Every edge and corner is labeled with its value and the area is shown. Change any input and the computation and drawing update immediately, so the triangle flexes as you edit.
The three facts may not describe any triangle: two angles that already sum to 180 deg or more leave no room for a third, and three sides form a triangle only when each is shorter than the sum of the other two. If both hold, the usual culprit is entering radians where the tool expects degrees.
That is the side-side-angle ambiguous case, and the double answer is correct. Because the sine of an angle equals the sine of its supplement, the same listed facts can fit two different triangles. Both are geometrically valid, so you choose the one matching the real object - for example, whether the unknown angle is acute or obtuse in your drawing.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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