\(\frac{X}{\sin 45^\circ} = \frac{15}{\sin 60^\circ}\)

\(X = \frac{15 \sin 45^\circ}{\sin 60^\circ}\)

\(X = \frac{15 \times \left( \frac{1}{\sqrt{2}} \right)}{\sqrt{\frac{3}{2}}}\)

\(X = \frac{15}{\sqrt{2}} \times \frac{2}{\sqrt{3}}\)

\(X = \frac{30}{\sqrt{6}}\)

\(X = \frac{30}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{30\sqrt{6}}{6} = 5\sqrt{6}\)