"Solving" a triangle means finding every side and angle from just three known values — and which formula you need depends entirely on which three values you're starting with.
What "Solving a Triangle" Means
Any triangle has six measurements: three sides and three angles. Knowing any three of them (as long as they're not all three angles, which doesn't fix a triangle's size) is enough to calculate the other three — but the method depends on which three you know.
SSS: Three Sides Known
When all three sides are known, the Law of Cosines finds each angle: c² = a² + b² − 2ab·cos(C), rearranged to solve for the angle instead of the side.
SAS: Two Sides and the Included Angle
When you know two sides and the angle between them, the Law of Cosines finds the third side directly, then the Law of Sines finds the remaining angles.
Right Triangles: A Simpler Special Case
| Known | Method |
|---|---|
| Two legs | Pythagorean theorem: c² = a² + b² |
| One leg + hypotenuse | Pythagorean theorem, solved for the missing leg |
| One side + one angle | Basic trigonometry (sine, cosine, tangent) |
Once You Have All Sides and Angles
With a fully solved triangle, area follows easily — either the classic ½ × base × height for right triangles, or Heron's formula (using all three sides) for any triangle regardless of type.
Step-by-Step: Solve Any Triangle
- Choose which three values you know: three sides, two sides and an angle, or a right triangle's legs
- Enter those known values
- Get every remaining side, angle, and the triangle's area
Try It Yourself
Use our free Triangle Calculator — SSS, SAS, and right triangle methods
Open Triangle Calculator →