1972 AHSME Problem 27

If the area of \triangle ABC is 64 square units and the geometric mean (mean proportional) between sides AB and AC is 12 inches, then \sin A is equal to

\textbf{(A) }\dfrac{\sqrt{3}}{2}\qquad \textbf{(B) }\frac{3}{5}\qquad \textbf{(C) }\frac{4}{5}\qquad \textbf{(D) }\frac{8}{9}\qquad \textbf{(E) }\frac{15}{17}

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