AHSME 1951 Problem 30

If two poles $20''$ and $80''$ high are $100''$ apart, then the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole is: $\textbf{(A)}\ 50'' \textbf{(B)}\ 40'' \textbf{(C)}\ 16'' \textbf{(D)}\ 60'' \textbf{(E)}\ \text{none of these}$