For the hypotenuse,
[tex]\begin{gathered} \cos \text{ 60 = }\frac{6\sqrt[]{3}}{y} \\ 0.\text{ 5 = }\frac{6\sqrt[]{3}}{y} \\ \\ y\text{ = }\frac{6\sqrt[]{3}}{0.5} \\ y\text{ = 12}\sqrt[]{3} \end{gathered}[/tex][tex]\begin{gathered} \text{For the short leg,} \\ \tan \text{ 30 = }\frac{x}{6\sqrt[]{3}} \\ \frac{1}{\sqrt[]{3}}\text{ = }\frac{x}{6\sqrt[]{3}} \\ \\ 1\text{ = }\frac{x}{6} \\ \text{ x = 1 x 6 = 6} \end{gathered}[/tex]