The resultant of two vectors is calculated by the formula R^2=P^2+Q^2+2PQcosΘ
The resultant of two vectors can be calculated by the vector parallelogram method, in which basic property of trigonometry is used to setup a simple formula for the resultant of two vectors.
Consider two vector P and Q, making an angle Θ from each other.
From right angled triangle OCD
OC^2=OD^2+DC^2
R^2=(OA+AD)^2+DC^2
R^2=OA^2+AD^2+2OA*AD+DC^2
From triangle ADC
AC^2=AD^2+CD^2, and cos Θ=AD/AC
R^2=OA^2+AC^2+2OA*AC*cosΘ
R^2=P^2+Q^2+2PQcosΘ