The drawing shows an equilateral triangle, each side of which has a length of $1\mathrm{.}09cm.$ Point charges are fixed to each corner, as shown.

The $4\mathrm{.}00C$ charge experiences a net force due to the charges $q_A$ and $q_B.$ This net force points vertically downward and has a

magnitude of $537$ N$.$ Determine $($a$)$ charge $q_A,($b$)$ charge $q_B.$