Let a,b be the lengths of the legs of the triangle (a > b > 0)

The hypotenuse of the triangle is : 15 x 2 = 30 (units)

\(\left\{{}\begin{matrix}ab=30.12\\a^2+b^2=30^2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a^2-2ab+b^2=180\\a^2+2ab+b^2=1620\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\left(a-b\right)^2=\left(6\sqrt{5}\right)^2\\\left(a+b\right)^2=\left(18\sqrt{5}\right)^2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a-b=6\sqrt{5}\\a+b=18\sqrt{5}\end{matrix}\right.\)

\(\Rightarrow2b=12\sqrt{5}\Rightarrow b=6\sqrt{5}\)

So, the answer is \(6\sqrt{5}\) units