Answer and Explanation:
We can solve for x and y using the ratio of sides in a 30-60-90 triangle:
1 : √3 : 2
For the smallest side, we are given the length:
[tex]\dfrac{3\sqrt5}{2}[/tex]
Based on the ratio of side lengths, we can multiply the smallest side length by [tex]\sqrt3[/tex] and [tex]2[/tex] to get [tex]y[/tex] and [tex]x[/tex], respectively:
[tex]y=\dfrac{3\sqrt5}{2} \times \sqrt3[/tex]
[tex]\boxed{y=\dfrac{3\sqrt{15}}{2}}[/tex]
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[tex]x=\dfrac{3\sqrt5}{2}\times 2[/tex]
[tex]\boxed{x=3\sqrt5}[/tex]
