About triangle calculator
Give the three side lengths and the calculator finds the angles and the area of the triangle.
Methods used
- Angles come from the law of cosines: cos A = (b² + c² − a²) ÷ 2bc.
- Area comes from Heron's formula: √(s(s − a)(s − b)(s − c)), where s is half the perimeter.
- The three angles always add up to 180 degrees.
Valid triangles
The longest side must be shorter than the sum of the other two. A 3, 4, 5 triangle works and has a right angle; a 1, 2, 5 set cannot form a triangle.
A worked example
Sides 3, 4 and 5 give angles of about 36.9, 53.1 and 90 degrees and an area of 6, so it is a right triangle. Sides 7, 8 and 9 have a semi-perimeter of 12 and an area of √(12 × 5 × 4 × 3) = √720, which is about 26.8.
Classifying
Three equal sides make an equilateral triangle, two equal an isosceles triangle, and none equal a scalene one. If a² + b² = c², the triangle has a right angle.
