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

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

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Answer 1 · 2015-05-31T16:54:03

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

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

then $R = {(A^{2} + B^{2} + 2 A B cos θ)}^{\frac{1}{2}}$ $R = (A^2 + B^2 + 2ABCos theta)^(1/2)$
where $θ$ $theta$ is the angle between A and B when they are drawn tail to tail.

This is the law of cosines.

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

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