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{15\sqrt2}{2}\\a\sqrt3=x\\\\a\sqrt3=\dfrac{15\sqrt2}{2}\qquad\text{multiply both sides by}\ \sqrt3\\\\3a=\dfrac{15\sqrt6}{2}\qquad\text{divide both sides by 3}\\\\a=\dfrac{5\sqrt6}{2}\\\\2a=2\cdot\dfrac{5\sqrt6}{2}=5\sqrt6[/tex]
Answer:
[tex]y=\dfrac{5\sqrt6}{2}\\\\x=5\sqrt6[/tex]
