$17 \cdot 57$ In $\triangle A B C$, $C D$ is the altitude on $A B$, $A E$ is the altitude on $B C$. If the lengths of $A B$, $C D$, and $A E$ are known, then the length of $D B$ is
(A) undetermined.
(B) determinable only if $A$ is an acute angle.
(C) determinable only if $\angle B$ is an acute angle.
(D) determinable only if $\triangle A B C$ is an acute triangle.
(E) none of the above.
(13th American High School Mathematics Examination, 1962)
[Solution] Consider the following cases:
(1) If $\angle A, \angle B$ are both acute angles ( $\angle C$ is acute, right, or obtuse). From $\triangle A B E \backsim \triangle C B D$, we can find $C B$ from the known values of $A B, C D, A E$. In the right triangle $\triangle C B D$, $B D$ can be found from $C B, C D$.
(2) If $\angle A$ is a right angle, the conclusion is the same as above.
(3) If $\angle B$ is an obtuse angle, we can find $B D$ from the similarity of right triangles $\triangle A B E \sim$ $\mathrm{Rt} \triangle C B D$.
(4) If $\angle A$ is a right angle, then $A B = B D$;
If $\angle B$ is a right angle, then $B D = 0$.
Therefore, the answer is $(E)$.