How to use (3 steps)
- Choose the mode (SSS, SAS, ASA/AAS or SSA) based on which sides and angles you know.
- Enter the known values and, if needed, adjust the angle unit and number of decimals.
- Results update automatically as you type. Use “Copy URL” to share the exact setup or switch between solutions when SSA gives two triangles.
How to use this calculator effectively
This guide helps you use Triangle Solver (SSS, SAS, ASA/AAS, SSA) with steps in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also
Results
Start with the sample or enter the known values. Results update automatically as you type.
This summary shows all sides, angles, area, radii, heights, medians, and angle bisectors for the triangle defined by your inputs.
Diagram
How it’s calculated
FAQ
Which inputs does this triangle solver support?
The calculator supports SSS, SAS, ASA/AAS, and SSA. SSA automatically checks whether zero, one, or two valid triangles exist and lets you switch between both solutions.
How are the steps calculated?
Angles and missing sides use the law of cosines or the law of sines depending on the mode. Every run shows Heron’s formula, semiperimeter, inradius, circumradius, heights, medians, and angle bisectors alongside an annotated diagram.
Why can SSA have two solutions (the ambiguous case)?
SSA means you know two sides and a non-included angle. Depending on the values, that angle can intersect the opposite side in two different places, producing two valid triangles. For an acute angle A with known a (opposite A) and b, compute h = b·sin(A): if a < h there is no triangle; if a = h there is one right triangle; if h < a < b there are two triangles; and if a ≥ b there is one triangle. If A is obtuse (> 90°), there can be at most one solution, and it exists only when a > b.
What makes a triangle impossible?
For SSS, the triangle inequality must hold: a + b > c, a + c > b, and b + c > a. For angle-based inputs, angles must sum to 180° (or π radians) and each angle must be between 0 and 180°. Measured values that are very close to the boundary can flip between valid and invalid due to rounding.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Worked examples & tips
- SSS (3-4-5): set a = 3, b = 4, c = 5 → a right triangle (C ≈ 90°), area ≈ 6.
- SSA two solutions: set A = 30°, a = 10, b = 12 → two valid triangles (B ≈ 36.87° or 143.13°).
- SSA no solution: set A = 30°, a = 5, b = 12 → no triangle (because the sine rule would require sin(B) > 1).
- Units check: if you enter angles in degrees, keep the angle unit as “Degrees” (switch to radians only if your angles are in radians).
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