Consider two vector A and B and their resulting A+B.the magnitude of the vector A and B are 13.2 and 8.2 they act at 45 degree to each other

Is your question to find the magnitude of the resultant vector, that is vector A+B?

I suggest you make a sketch, making it as close as possible to the given measurements. Draw the resultant vector, and use the method of parallelogram of vectors to get a parallelogram and giving you triangles with which you can work with, using the cosine rule most probably.