Triangle Solver
Solve SSS, SAS, ASA, AAS and SSA triangles, including the ambiguous case, with area, perimeter, heights and a drawing.
🔒 Runs entirely in your browser — nothing is uploadedSolving a triangle from three known values
A triangle has three sides and three angles, but you only need three of those six values, with at least one of them a side, to determine the rest. This solver handles the five standard cases. With SSS the three sides are known and the law of cosines gives the angles. With SAS two sides and the angle between them give the third side through the law of cosines. With ASA and AAS two angles fix the third, because angles add up to 180 degrees, and the law of sines then produces the remaining sides. By convention side a lies opposite angle A, side b opposite B and side c opposite C.
The ambiguous SSA case
Knowing two sides and an angle that is not between them, called SSA, is special because it does not always identify a single triangle. Let A be the given angle, a its opposite side and b the other given side. The height from the far vertex to the base is b·sin A. If a is shorter than that height, the side cannot reach the base and no triangle exists. If a equals the height you get exactly one right triangle. If A is acute and a lies between the height and b, two different triangles fit: one with an acute angle B and one with the obtuse supplement 180° − B. If a is at least as long as b, only one triangle works. The solver tests every branch and lists each valid solution in its own card with its own drawing.
What you get in the results
Besides the missing sides and angles, the tool reports the area, computed from two sides and the included angle, the perimeter, and the three heights, each equal to twice the area divided by the matching side. It also gives the inscribed circle radius and the circumscribed circle radius, and classifies the triangle by its sides (equilateral, isosceles or scalene) and by its angles (acute, right or obtuse). The drawing is scaled to fit and labels every vertex angle and side length, which makes it easy to spot a typing error such as a swapped value. Inputs are validated before solving, so impossible combinations produce a clear explanation instead of a wrong answer. Results are shown with up to eight significant digits, and all calculations run in your browser without sending anything over the network.
How to use
- Choose what you knowSelect SSS, SAS, ASA, AAS or SSA depending on which sides and angles are given.
- Enter the valuesFill in the visible fields and pick degrees or radians. Side a is opposite angle A, b opposite B, c opposite C.
- SolvePress solve to get every missing side and angle, plus area, perimeter, heights and the triangle type.
- Check the drawingCompare the scaled drawing with your figure. In the SSA case, look at both solutions when two exist.