The drawing shows an equilateral triangle, each side of which has a length of $4\mathrm{.}23cm.$ 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 $581N.$ Determine a$)$ charge $q_A,$ b$)$ charge $q_B.$