Question

How can the law of cosines be used to find the magnitude of a resultant?

Answer 1

If we are to add vector A and B and if `A` and `B` be their magnitudes, then

If R is the resultant and `R` it's magnitude,

then `R = (A^2 + B^2 + 2ABCos theta)^(1/2)`
where `theta` is the angle between A and B when they are drawn tail to tail.

This is the law of cosines.