Triangle Solver
How It Works
This triangle solver uses established formulas to provide accurate results.
The basic rule:
- Law of Cosines: c² = a² + b² - 2ab·cos(C)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Angle sum: A + B + C = 180°
- Area = ½ab·sin(C)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What does SSS, SAS, ASA, and AAS mean?
These abbreviations describe which parts of a triangle you know. SSS = three sides, SAS = two sides and the included angle, ASA = two angles and the included side, AAS = two angles and a non-included side.
When do I use Law of Cosines vs Law of Sines?
Use the Law of Cosines for SSS and SAS problems (when you know two or more sides). Use the Law of Sines for ASA and AAS problems (when you know two angles). Both can sometimes be used in combination.
Can a triangle have angles summing to more than 180 degrees?
In Euclidean (flat) geometry, the angles of a triangle always sum to exactly 180°. If your inputs sum to more than 180°, the triangle is not valid.
What is the ambiguous case (SSA)?
The SSA case (two sides and a non-included angle) can yield zero, one, or two valid triangles. This calculator handles the primary solution; check whether a second triangle exists by seeing if 180° minus the found angle also yields a valid triangle.