MathNet 2022-part-06 — 196 problems (EN–VI) Question 111

Isosceles trapezoid $ABCD$ with bases $AB$ and $CD$ has a point $P$ on $AB$ with $AP=11$, $BP=27$, $CD=34$, and $\angle CPD=90^{\circ}$. Compute the height of isosceles trapezoid $ABCD$.