Given: vector $x_{?}$ by its magnitude $x$ and direction ${}_x$ and vector $Y_{?}$ by its magnitude $Y$ and direction ${}_Y,$ determine the resultant $Z_{?}=x_{+}{Y}_{?}$ by declaring its magnitude $Z$ and direction ${}_Z.$ Do this by using the triangles $($and

their laws$)$ embedded in the above parallelogram law, finding the interior angles $lo{n}_Z$ and $lo{n}_x.$

First Example. Given $x=2\mathrm{.}500in$ and ${}_x=15\mathrm{.}000$deg and $Y=1\mathrm{.}000in$ and ${}_Y=90\mathrm{.}000$deg, declare the unknown values. Be sure to keep angles between $-180$deg and $+180$ deg $.$