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**HallsofIvy** First, what do you mean by "addition of two vector magnitudes". If you mean "find the magnitude of the sum of two vectors, having magnitudes A and B", then what you give is true only if the two vectors are perpendicular- it is from the Pythagorean theorem which applies to right triangles.

This is the magnitude of the sum of two vectors having magnitudes A and B which form angle $\displaystyle \theta$, not necessarily perpendicular. Notice that if $\displaystyle \theta= \pi/2$, then $\displaystyle cos(\theta)= 0$ so you get the same thing as before. It is from the cosine law that generalizes the Pythagorean theorem to general triangles.