In order to calculate the length of the long leg, we can use the sine relation of the 60° angle.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (60\degree)=\frac{x}{6\sqrt[]{10}} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{6\sqrt[]{10}} \\ 2x=6\sqrt[]{30} \\ x=3\sqrt[]{30} \end{gathered}[/tex]So the length of the long leg is 3√30 yd.
