A triangle has six parts, three sides and three angles, and knowing any three of them (with at least one side) is usually enough to find the rest. Fill in what you know and this calculator finds every side and angle, the perimeter and the area, and names the triangle. When your values fit two different triangles, it shows both.
How to Use It
- Look at the diagram: side a faces angle A, b faces B and c faces C.
- Fill in exactly three boxes, at least one of them a side, and leave the other three blank.
- Optionally choose a Unit to label the answers.
- Press Calculate to see every side and angle, the perimeter, the area and the type of triangle.
How It Works
Which rule the calculator uses depends on what you know:
- SSS (three sides) and SAS (two sides and the angle between them) use the law of cosines:
- ASA and AAS (two angles and a side) find the third angle from , then use the law of sines:
- SSA (two sides and an angle not between them) also uses the law of sines, but it can give no triangle, one, or two. That’s the ambiguous case, and the calculator shows every triangle that fits.
The area comes from Heron’s formula, with s as half the perimeter:
Worked Example
A triangle has sides b = 4 and c = 5 with A = 60° between them (SAS). The law of cosines gives the third side:
With all three sides known, the law of cosines gives the other angles: B ≈ 49.107° and C ≈ 70.893°.
Tips and Common Mistakes
- Match sides to opposite angles. Side a always faces angle A; mixing them up gives a different triangle.
- Use degrees. Convert radians first: multiply by 180 and divide by π.
- Three angles aren’t enough. They fix the shape but not the size, so include a side.
- Expect two answers in SSA. If your class problem says “find all triangles,” the ambiguous case is the reason.
- Check the triangle inequality. Each side must be shorter than the other two added together, or there’s no triangle.