$\begin{align}  & \text{Using sine rule} \\ & \frac{x}{\sin {{45}^{o}}}=\frac{15}{\sin {{60}^{o}}} \\ & x=\frac{15\sin {{45}^{o}}}{\sin {{60}^{o}}}=\frac{15\times \tfrac{1}{\sqrt{2}}}{\tfrac{\sqrt{3}}{2}}=\frac{15\times 2}{\sqrt{3}\times \sqrt{2}}=\frac{30}{\sqrt{6}} \\ & x=\frac{30}{\sqrt{6}}\times \frac{\sqrt{6}}{\sqrt{6}}=\frac{30\sqrt{6}}{6}=5\sqrt{6} \\\end{align}$