We have the triangle 30° - 60° - 90°.
The lenght of the sides are in proportion: [tex]1:2:\sqrt3\to a:2a:a\sqrt3[/tex].
[tex]a=y\\2a=\dfrac{\sqrt2}{3}\\\\a\sqrt3=x\\\\2a=\dfrac{\sqrt2}{3}\qquad\text{divide both sides by 2}\\\\a=\dfrac{\sqrt2}{6}\\\\a\sqrt3=\dfrac{\sqrt2}{6}\cdot\sqrt3=\dfrac{\sqrt6}{6}[/tex]
Answer:
[tex]A)\ x=\dfrac{\sqrt6}{6},\ y=\dfrac{\sqrt2}{6}[/tex]
