A triangle has six parts or elements - the sides a, b, c and the angles A, B, C.
The process of finding the unknown parts of a triangle is called the solution of triangle. If three parts of a triangle (at least one of which is a side) are given then the other parts can be found.
Type I: Three sides (SSS) are given
To solve this type, you can use any one of the following formulae.
- Cosine formula
- Sine formula
- Half angle formula
It is better to use cosine formula if the sides are small, while use half angle formula if the sides are large.
Type II: One side and any two angles (SAA) are given
To solve this type, find the third angle and use the sine formula.
Type III: Two sides and the included angle (SAS) are given
Since two sides and the included angle are given, the third side can be found by using the proper cosine formula. Then, you can apply the sine formula to calculate the other elements.