Find the value of x and the value of y.A. x= 2 root 2, y = 8B. X= 2, y = 4 root 6C. X = 2 root 2, y=2 root 6D. X = 2 root 3, y=6 root 3

Answer:Option C.[tex]x=2\sqrt{2}[/tex][tex]y=2\sqrt{6}[/tex]Step-by-step explanation:step 1Find the value of xIn the right triangle of the figure[tex]sin(30\°)=\frac{x}{4\sqrt{2}}[/tex] -----> opposite side angle of 30 degrees divided by the hypotenuseRemember that[tex]sin(30\°)=\frac{1}{2}[/tex] so[tex]\frac{1}{2}=\frac{x}{4\sqrt{2}}[/tex][tex]x=\frac{4\sqrt{2}}{2}[/tex][tex]x=2\sqrt{2}[/tex]step 2Find the value of yIn the right triangle of the figure[tex]cos(30\°)=\frac{y}{4\sqrt{2}}[/tex] -----> adjacent side angle of 30 degrees divided by the hypotenuseRemember that[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]so[tex]\frac{\sqrt{3}}{2}=\frac{y}{4\sqrt{2}}[/tex][tex]y=\frac{4\sqrt{6}}{2}[/tex][tex]y=2\sqrt{6}[/tex]