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Triangle Calculator
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Enter all three side lengths to find the area, perimeter, and angles.
| Perimeter | 18 |
| Area | 14.98 |
| Angle A (opposite a) | 44.42° |
| Angle B (opposite b) | 57.12° |
| Angle C (opposite c) | 78.46° |
Solving a Triangle From Three Sides (SSS)
When all three side lengths are known, the area can be found without needing any angles first, using Heron's formula. Once the area is known, each angle can be found using the law of cosines, rearranged to solve for the angle directly.
Area = √( s(s−a)(s−b)(s−c) )
where s = (a+b+c) / 2 is the semi-perimeter
cos(A) = (b² + c² − a²) ÷ (2bc)
Triangle Inequality
Three lengths only form a valid triangle if the sum of any two sides is greater than the third side. This calculator checks that automatically and will let you know if the sides you entered can't form a real triangle.