We have a right triangle with a 60 degree angle so this is 30/60/90, half an equilateral triangle, one of the two tired triangles of trig. I could solve it for the thousandth time or just tell you the truth: you need to memorize this one and the other one, 45/45/90, half a square. It's two lousy triangles; you'll be done in ten minutes. But it's ten minutes well spent.
The sides of 30/60/90 are in ratio [tex]1:\sqrt{3}:2[/tex] and here [tex]y:x:10\sqrt{3}[/tex] so
[tex] \dfrac{y}{1} = \dfrac{x}{\sqrt{3}} = \dfrac{10\sqrt{3}}{2}[/tex]
[tex]x = \sqrt{3} \cdot \dfrac{10\sqrt{3}}{2} = 15[/tex]
[tex]y = 5\sqrt{3}[/tex]
Answer: x=15, y=5√3
