Two vectors add head to tail: slide the second one's tail onto the first one's head, and the resultant is the arrow from the very start to the very end. Do that with lengths $A$ and $B$ and an angle $\theta$ between them — measured tail to tail, the way the two arrows leave the same point — and the resultant's length is $R = \sqrt{A^2 + B^2 + 2AB\cos\theta}$. Read aloud: R equals the square root of A squared plus B squared plus two A B cos theta. $A$ and $B$ are the two magnitudes in the story's unit, $R$ comes out in that same unit, and $\theta$ is the only thing here wearing degrees.

Note the $+$. Its cousin, the law of cosines $c^2 = a^2 + b^2 - 2ab\cos C$, carries a minus — because $C$ is the TRIANGLE's interior angle, which is $180^\circ - \theta$ once you slide the second arrow into place. Same geometry, two conventions; mixing them computes $\vec{a} - \vec{b}$ with total confidence and hands you a wrong number. The rail that catches nearly every slip: R always lands between $|A - B|$ and $A + B$ — dead against at $180^\circ$, dead together at $0^\circ$, everything else in between. Which is why simply adding the magnitudes is only right in the one case where the arrows are parallel.