HMMT November 2022 U11

Isosceles trapezoid $A B C D$ with bases $A B$ and $C D$ has a point $P$ on $A B$ with $A P=11, B P=27$, $C D=34$, and $\angle C P D=90^{\circ}$. Compute the height of isosceles trapezoid $A B C D$.