Triangle Solver

What this tool does

Give the triangle solver three known sides (SSS), two sides and the included angle (SAS), or two angles and the included side (ASA), and it computes every remaining side, angle, the area and the perimeter. Inputs are validated against the triangle inequality and the 180-degree angle sum before solving.

Not every triangle is a right triangle, so general problems need the law of cosines and the law of sines rather than the Pythagorean theorem alone. This solver accepts the three classic combinations of known measurements — three sides (SSS), two sides with the included angle (SAS), or two angles with the included side (ASA) — and fills in everything else.

Once solved, you get all three sides, all three angles, the total area and the perimeter in one view, each traceable back to the law applied. Invalid input, like sides that cannot physically form a triangle or angles that do not leave room for a third, is rejected with a clear explanation rather than a silent wrong answer.

How to use Triangle Solver

1. Pick the combination of known values that matches your problem: SSS, SAS or ASA.
2. Enter the known side lengths and/or angle in degrees into the fields shown.
3. For SAS, make sure the angle you enter is the one between the two given sides, not one of the other two.
4. For ASA, make sure the side you enter is the one between the two given angles.
5. Read off the three sides, three angles, area and perimeter from the results.
6. Check the note confirming the three angles sum to 180° as a sanity check on the solve.

Tips for better results

• SAS requires the included angle specifically — the angle sitting between the two sides you measured, not an angle at one of their far ends.
• ASA requires the included side — the one connecting the two vertices where your two known angles sit.
• For SSS, if the triangle inequality fails (the two shorter sides do not add up to more than the longest), the tool throws a clear error instead of returning nonsense angles.
• Area in SAS and ASA mode is computed directly from two sides and the sine of the angle between them, which is often faster than Heron’s formula once you already have that angle.
• All angle inputs and outputs are in degrees, not radians.

Common use cases

• Solving triangulation or surveying problems where distances and one angle, or two angles and a baseline, are measured in the field.
• Working through trigonometry homework involving the law of cosines or law of sines.
• Finding the area of an irregular triangular plot of land from two sides and the angle between them.
• Checking whether a set of three measured side lengths could plausibly describe a real triangle before trusting further calculations on it.

Common mistakes to avoid

• Entering a non-included angle for SAS, which silently uses the wrong law of cosines setup and produces an incorrect triangle.
• Entering a non-included side for ASA, the mirror-image mistake of the SAS case above.
• Supplying three sides that violate the triangle inequality and expecting a result instead of the explanatory error this tool raises.
• Mixing up degrees and radians when double-checking the solver’s angle outputs against another formula or calculator.