We have a right triangle, of which we know one angle measure and one of the leg's length.
We can use trigonometric ratios to find x and y.
For example, we can relate the two legs with the tangent of the angle as:
[tex]\begin{gathered} \tan (\alpha)=\frac{\text{Opposite}}{\text{Adyacent}} \\ \tan (60\degree)=\frac{11\sqrt[]{3}}{x} \\ x=\frac{11\sqrt[]{3}}{\tan(60\degree)}=\frac{11\sqrt[]{3}}{\sqrt[]{3}}=11 \end{gathered}[/tex]
Then, we can relate x and y as:
[tex]\begin{gathered} \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (60\degree)=\frac{x}{y}=\frac{11}{y} \\ y=\frac{11}{\cos(60\degree)}=\frac{11}{\frac{1}{2}}=11\cdot2=22 \end{gathered}[/tex]
Answer: x=11 and y=22.
