In a 30-60-90 triangle, the shorter side is represented as [tex]s[/tex], the hypotenuse as [tex]2s[/tex], and the longer side as [tex]s \sqrt{3}[/tex]. Since we are given the hypotenuse's length, we can use it to solve for [tex]s[/tex]:
[tex]2s = 30 \\ s = 15[/tex]
We now have the value of the shorter side, or [tex]x[/tex] in your diagram - 15 units. Next, we can use [tex]s[/tex] to solve for the long side's length:
[tex]s \sqrt{3} = y \\
15 \sqrt{3} = y[/tex]
The length of the longer side, [tex]y[/tex], is [tex]15 \sqrt{3} [/tex] (approxiamtely 26) units.
