AMC 12 2025b Problem 10

The altitude to the hypotenuse of a $30{-}60{-}90^\circ$ is divided into two segments of lengths $x<y$ by the median to the shortest side of the triangle. What is the ratio $\tfrac{x}{x+y}$?

$\textbf{(A) } \dfrac{3}{7} \textbf{(B) } \dfrac{\sqrt3}{4} \textbf{(C) } \dfrac{4}{9} \textbf{(D) } \dfrac{5}{11} \textbf{(E) } \dfrac{4\sqrt3}{15}$