We have hypothenuse which I will denote with [tex]h=6\sqrt{3}[/tex] and angle [tex]\beta=30^{\circ}[/tex].
First we can use the sine function to determine the length of [tex]x[/tex] by solving the following equality:
[tex]\sin(\beta)=\dfrac{x}{h}\implies x=\sin(\beta)h=\boxed{3\sqrt{3}}[/tex].
Simlarly, we can find [tex]y[/tex] using cosine function:
[tex]\cos(\beta)=\dfrac{y}{h}\implies y=\cos(\beta)h=\boxed{9}[/tex].
Hope this helps.
