For this case we have, by definition of trigonometric relationships of rectangular triangles that the sine of an angle is given by the opposite leg to the angle on the hypotenuse. So, according to the figure we have:
[tex]Sin (30) =\frac {y} {12\sqrt {3}}\\y = Sin (30) * 12 \sqrt {3}\\y = \frac {1} {2} * 12 \sqrt {3}\\y = 6 \sqrt {3}[/tex]
Through the Pythagorean theorem we can find the value of "x":
[tex]x = \sqrt {(12 \sqrt {3}) ^ 2- (6 \sqrt {3}) ^ 2}\\x = \sqrt {144 * 3-36 * 3}\\x = \sqrt {432-108}\\x = \sqrt {324}\\x = 18[/tex]
ANswer:
[tex]y=6\sqrt{3}\\x=18[/tex]
