1979 AHSME Problem 24

Sides AB,~ BC, and CD of (simple*) quadrilateral ABCD have lengths 4,~ 5, and 20, respectively. If vertex angles B and C are obtuse and \sin C = - \cos B =\frac{3}{5}, then side AD has length

- A polygon is called “simple” if it is not self intersecting.

\textbf{(A) }24\qquad \textbf{(B) }24.5\qquad \textbf{(C) }24.6\qquad \textbf{(D) }24.8\qquad \textbf{(E) }25

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.