How to solve a triangle
Solving a triangle means finding all of its sides and angles from just three measurements, as long as at least one of them is a side. The calculator uses the law of cosines when you provide sides and the law of sines when you provide angles.
The three main cases
With three sides, the angles come from the law of cosines, cos A = (b² + c² − a²) / (2bc). With two sides and the included angle, the third side is c² = a² + b² − 2ab × cos C. With two angles and a side, the third angle is 180° minus the other two, and the remaining sides follow from the law of sines.
Types of triangles
By sides, a triangle is equilateral (all three equal), isosceles (two equal), or scalene (all different). By angles, it is acute (all under 90°), right (one angle of 90°), or obtuse (one angle over 90°). The interior angles always add up to 180°.
Practical example
Two fences of 5 m and 7 m start at the same corner and meet at a 60° angle. The distance between their far ends is about 6.245 m, and the triangular plot between them covers roughly 15.16 m².