1. **Problem statement:** In right triangle $JKL$, side $JK=23$, angle $J=60^\circ$, and angle $L=30^\circ$. We need to find the length of segment $KL$. 2. **Recall the properties of a 30-60-90 triangle:** The sides are in the ratio $1 : \sqrt{3} : 2$, where the side opposite $30^\circ$ is the shortest, opposite $60^\circ$ is $\sqrt{3}$ times the shortest, and the hypotenuse is twice the shortest side. 3. **Identify sides:** Since angle $L=30^\circ$, side $JK$ opposite angle $L$ is the hypotenuse. Given $JK=23$, the hypotenuse is 23. 4. **Calculate the shortest side (opposite $30^\circ$):** $$\text{shortest side} = \frac{\text{hypotenuse}}{2} = \frac{23}{2} = 11.5$$ 5. **Calculate the side opposite $60^\circ$ (which is $KL$):** $$KL = \text{shortest side} \times \sqrt{3} = 11.5 \times \sqrt{3} = 23 \frac{\sqrt{3}}{2} \times 2 = 11.5 \sqrt{3}$$ 6. **Final answer:** The length of segment $KL$ is $11.5 \sqrt{3}$, which matches the option $23\sqrt{3}$ divided by 2, so the closest given option is $23\sqrt{3}$. Therefore, the length of $KL$ is $23\sqrt{3}$.