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.
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
Use this page when a triangle is fixed by measured sides and angles
Triangle Solver is the right page when you already know an SSS, SAS, ASA/AAS, or SSA setup and need the full triangle plus worked steps. Open 2D Geometry for other shapes, use Unit Circle for core trig identities, and switch to Vector Calculator when the problem is coordinate or dot-product based instead of classical triangle solving.
- Pick the input mode first so only the valid fields stay active.
- Check the angle unit before comparing degree-based and radian-based work.
- Use the diagram and step log together when SSA ambiguity is possible.
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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