Triangle Calculator
Enter any three values that fix a triangle — sides, angles or a mix — and get every missing side and angle, the area, perimeter, heights and a to-scale drawing.
Method: Law of cosines for each angle. Side a is opposite angle A, and so on.
- Sides a · b · c
- 5 · 7 · 9
- Angles A · B · C
- 33.56° · 50.7° · 95.74°
- Perimeter
- 21
- Type
- scalene, obtuse
- Height to c
- 3.8694
- Inradius · circumradius
- 1.6583 · 4.5227
Which three values solve a triangle?
- SSS — three sides. Angles come from the law of cosines: cos A = (b² + c² − a²) / 2bc.
- SAS — two sides and the angle between them. Law of cosines gives the third side: c² = a² + b² − 2ab cos C.
- ASA / AAS — two angles and a side. The third angle is 180° minus the other two; the law of sines, a / sin A = b / sin B = c / sin C, gives the sides.
- SSA — two sides and an angle not between them. This is the "ambiguous case": zero, one or two triangles can fit, and the calculator shows both when two do.
- AAA — three angles fix the shape but not the size, so you always need at least one side.
For right triangles, the right triangle calculator is quicker — two values are enough.
Questions people ask
How do I find the area of a triangle with three sides?
Use Heron's formula. With s = half the perimeter, area = √(s(s−a)(s−b)(s−c)). For sides 5, 7, 9: s = 10.5 and area ≈ 17.41.
Why does SSA sometimes give two answers?
The side opposite the known angle can swing to meet the base at two different points, producing one acute and one obtuse triangle. If it is too short it misses entirely.
Can a triangle have sides 2, 3 and 6?
No. By the triangle inequality, any two sides must add up to more than the third, and 2 + 3 < 6.
Do the angles have to add to 180°?
Yes, in flat (Euclidean) geometry. On a sphere, like the Earth's surface, they add to more.
Stuck on a word problem?
Paste a homework question or describe your project. The AI tutor names the formula and works it through step by step. Always check the result with the calculator above.