Triangle F G H is similar to triangle J K L , where angle F corresponds

Choice B is correct. If two triangles are similar, then their corresponding angles are congruent. It's given that right triangle $FGH$ is similar to right triangle $JKL$ and angle $F$ corresponds to angle $J$. It follows that angle $F$ is congruent to angle $J$ and, therefore, the measure of angle $F$ is equal to the measure of angle $J$. The sine ratios of angles of equal measure are equal. Since the measure of angle $F$ is equal to the measure of angle $J$, $\sin \left(F\right)=\sin \left(J\right)$. It's given that $\sin \left(F\right)=\frac{308}{317}$. Therefore,  $\sin \left(J\right)$ is $\frac{308}{317}$.

Choice A is incorrect. This is the value of $\cos \left(J\right)$, not the value of $\sin \left(J\right)$.

Choice C is incorrect. This is the reciprocal of the value of $\sin \left(J\right)$, not the value of $\sin \left(J\right)$.

Choice D is incorrect. This is the reciprocal of the value of $\cos \left(J\right)$, not the value of $\sin \left(J\right)$.