In triangle \( JKL \), we know that \( \angle J = 60^\circ \), \( \angle L = 30^\circ \), and the length of side \( JK = 57 \).
Since this is a right triangle, we can use the properties of 30-60-90 triangles to find the length of segment \( JL \).
In a 30-60-90 triangle:
- The side opposite the 30-degree angle is half the hypotenuse.
- The side opposite the 60-degree angle is \(\sqrt{3}\) times the length of the side opposite the 30-degree angle.
Here, side \( JL \) is opposite angle \( K \), which is 30 degrees, and side \( JK \) is opposite angle \( L \), which is 60 degrees.
Thus:
- Side \( KL \) (which is opposite angle \( J \)) is the hypotenuse, so \( KL = JK = 57 \).
- According to the property of a 30-60-90 triangle, the length of side \( JL \) (which is opposite the 30-degree angle) will be:
\[ JL = \frac{1}{2} \times KL = \frac{1}{2} \times 57 = 28.5 \]
Thus, the length of segment \( JL \) is \( \boxed{28.5} \).