Triangles $△CDE$ and $△FGH$ are similar with right angles at $D$ and $G$, and corresponding sides $CD\leftrightarrow FG$, $DE\leftrightarrow GH$, $CE\leftrightarrow FH$. If $CD=4.5$, $DE=6$, $CE=7.5$, and $FG=3$, find $FH$.