The drawing shows an equilateral triangle, each side of which has a length of $1\mathrm{.}28cm.$ 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 $312N.$ Determine $($a$)$ charge $q_A,($b$)$ charge $q_B.$

$($a$)$ Number

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$($b$)$ Number

Units