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