AHSME 1962 Problem 23

In triangle $ABC$, $CD$ is the altitude to $AB$ and $AE$ is the altitude to $BC$. If the lengths of $AB$, $CD$, and $AE$ are known, the length of $DB$ is:

$\textbf{(A)}\ \text{not determined by the information given}$ $\textbf{(B)}\ \text{determined only if A is an acute angle}$ $\textbf{(C)}\ \text{determined only if B is an acute angle}$ $\textbf{(D)}\ \text{determined only if ABC is an acute triangle}$ $\textbf{(E)}\ \text{none of these is correct}$