Answer
Both methods find that the magnitude of $u+v$ is $9.5$ and the direction is $119^{\circ}$
Work Step by Step
When we use the law of cosines and the law of sines to find $u+v$, the magnitude is $9.5$ and the direction is $119^{\circ}$
When we use vector components to find $u+v$, the magnitude is $9.5$ and the direction is $119^{\circ}$
As expected, both methods yield the same result.
