A triangle is a geometrical object that has three angles, hence the name tri–angle. Any valid plane triangle must adhere to the following two rules: (1) the sum of two sides of a triangle must be greater than the third side, and (2) the sum of the angles of a plane triangle must be equal to 180°. In order to define a triangle one of the following four data sets must be given: (a) 1 side and 2 angles, or (b) 2 sides and an angle between them, or (c) 2 sides and an angle opposite one of the sides, or finally (d) 3 sides.
The triangle area A and all other triangle’s attributes are calculated using 3 sides. This is a right triangle since angle γ is equal to 90°. This is a scalene triangle: no equal sides and no equal angles.
The calculator uses the Sine Law [ a ⁄ sin α = b ⁄ sin β = c ⁄ sin γ ] to calculate a triangle second angle, when two sides and an angle opposite one of them are given. Then, the calculator uses the projection rule to calculate the triangle third side: c = a cos β + b cos α.
The calculator uses the Cosine Law [ c² = a² + b² − 2ab cos γ ] to calculate a triangle third side, when two sides and an angle between them are given.
When one side and two angles are given, the calculator uses the rule that the sum of the angles of a plane triangle must be equal to 180° to calculate the remaining third angle.
The calculator uses the Heron’s formula to calculate a triangle area A = √s(s−a)(s−b)(s−c), where s is the triangle semiperimeter.