2^{\circ}$ and $b = 5.7$. We know that in a right triangle, the sum of the other two angles is $90^{\circ}$. Therefore, we can find $\angle B$ by subtracting $\angle A$ from $90^{\circ}$:
\[m \angle B = 90^{\circ} - 34.2^{\circ} = 55.8^{\circ}\]
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