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Triangle Solver (SSS / SAS / ASA)

Select the known combination (three sides, two sides plus the included angle, or two angles plus the included side) and this tool will compute the remaining.

Need step-by-step derivations or ambiguous SSA handling? Use the advanced triangle solver.

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Known values

Used in SSS and SAS; for SAS it is one of the sides adjacent to angle C.

In SAS this is the other side adjacent to angle C.

Used in SSS and as the included side between angles A and B in ASA.

First known angle for the ASA mode.

Second known angle for the ASA mode.

SAS uses the included angle between sides a and b.

Enter your known values and click “Solve triangle” to see the computed sides, angles, area, and radii here.

FAQ

Which input combinations are supported?

You can pick SSS, SAS, or ASA. Ambiguous SSA cases are intentionally excluded to keep the output deterministic.

How do you compute the area and radii?

Once all three sides are known, the solver uses Heron’s formula for the area, then derives the circumradius with R = abc / (4S) and the inradius with r = S / s.

Do you validate impossible triangles?

Yes. The calculator checks the triangle inequality and the 180° interior-angle sum before showing any results.

What should I enter first?

Start with the minimum required inputs shown above the calculate button, then keep optional settings at their defaults for a first pass. After getting a baseline, change one parameter at a time so you can explain which assumption moved the output.

How precise are the results?

The calculator keeps internal precision and rounds only for display. Small differences can still appear if another tool uses different constants, period conventions, or rounding rules. Align assumptions before comparing final values.

How to use Triangle Solver (SSS / SAS / ASA) effectively

What this calculator does

This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.

Input meaning and unit policy

Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.

Use-case sequence

A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.

Common mistakes to avoid

Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.

Interpretation guidance

Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.