$(0)$ Vector vec$(C)$ has a magnitude of $25\mathrm{.}8m$ and points in the $-y$ direction. Vectors vec$(A)$ and vec$(B)$ both have positive $y-$components, and make angles of $=41\mathrm{.}4$ and $=29\mathrm{.}2$ with the positive and negative $x-$axis, respectively.

If the vector sum vec$(A)+$vec$(B)+$vec$(C)=0,$ what are the magnitudes of vec$(A)$ and vec$(B)?$