smc

Since the three angles of a triangle add up to $180^{\circ }$ and one of the angles is $90^{\circ }$ because it's a right triangle, $a^{\circ }+b^{\circ }=90^{\circ }$. The greatest prime number less than $90$ is $89$. If $a=89^{\circ }$, then $b=90^{\circ }-89^{\circ }=1^{\circ }$, which is not prime. The next greatest prime number less than $90$ is $83$. If $a=83^{\circ }$, then $b=7^{\circ }$, which IS prime, so we have our answer $\boxed{7}$