Find the value of x and y. ( ANSWER NEEDS TO BE IN REDUCED RADICAL FORM )

Answer:Part 1) [tex]x=8\sqrt{2}\ units[/tex]Part 2) [tex]y=4\sqrt{6}\ units[/tex]Step-by-step explanation:see the attached figure with letters to better understand the problemIn the right triangle ABDFind the length side BD[tex]sin(45\°)=BD/AB[/tex][tex]BD=(AB)sin(45\°)[/tex]we have[tex]AB=8\ units[/tex][tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]substitute the given values[tex]BD=(8)\frac{\sqrt{2}}{2}[/tex][tex]BD=4\sqrt{2}\ units[/tex]In the right triangle DBCFind the length side BC[tex]sin(30\°)=BD/BC[/tex][tex]BC=BD/sin(30\°)[/tex]we have[tex]sin(30\°)=\frac{1}{2}[/tex][tex]BD=4\sqrt{2}\ units[/tex]substitute the given values[tex]BC=4\sqrt{2}/\frac{1}{2}[/tex][tex]BC=8\sqrt{2}\ units[/tex]thereforeThe value of x is [tex]x=8\sqrt{2}\ units[/tex]In the right triangle DBCFind the length side DC[tex]cos(30\°)=DC/BC[/tex][tex]DC=(BC)cos(30\°)[/tex]we have[tex]BC=8\sqrt{2}\ units[/tex][tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]substitute the given values[tex]DC=(8\sqrt{2})\frac{\sqrt{3}}{2}[/tex][tex]DC=4\sqrt{6}\ units[/tex]thereforethe value of y is[tex]y=4\sqrt{6}\ units[/tex]