1988 AHSME Problem 24

An isosceles trapezoid is circumscribed around a circle. The longer base of the trapezoid is 16, and one of the base angles is \arcsin(.8). Find the area of the trapezoid.

\textbf{(A)}\ 72\qquad \textbf{(B)}\ 75\qquad \textbf{(C)}\ 80\qquad \textbf{(D)}\ 90\qquad \textbf{(E)}\ \text{not uniquely determined}

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