

\begin{align*}
ABC\text{ rectangle en }A & \iff BC^2 = AB^2 + AC^2\\[2ex]
& \iff \big(x_C-x_B\big)^2+\big(y_C-y_B\big)^2 = \Big[ \big(x_B-x_A\big)^2+\big(y_B-y_A\big)^2 \Big]\\[2ex]
& \hspace*{7cm} + \Big[ \big(x_C-x_A\big)^2+\big(y_C-y_A\big)^2 \Big]\\[2ex]
& \iff (3-1)^2+(y+2)^2 = \Big[(1+3)^2 + (-2-5)^2\Big] + \Big[(3+3)^2 + (y-5)^2\Big]\\[2ex]
& \iff 4+\cancel{y^2}+4y+4=16+49+36+\cancel{y^2}-10y+25\\[2ex]
& \iff 4y+10y=16+49+36+25-4-4\\[2ex]
& \iff 14y = 118\\[2ex]
& \iff \boxed{y = \dfrac{118}{14}=\dfrac{59}{7}}
\end{align*}
