MathNet 2019-part-08 — 179 problems (EN–VI) Question 46

Let $ABCD$ be an isosceles trapezoid with $AD = BC = 255$ and $AB = 128$. Let $M$ be the midpoint of $CD$ and let $N$ be the foot of the perpendicular from $A$ to $CD$. If $\angle MBC = 90^{\circ}$, compute $\tan \angle NBM$.