3. In $\triangle A B C$, it is known that $\angle A=a, C D$ and $B E$ are the altitudes on $A B$ and $A C$ respectively, then $\frac{D E}{B C}=$ $\qquad$
3. $\because \angle B D C=\angle B E C$,
$\therefore B, D, E, C$ are concyclic,
$\angle A D E=\angle A C B$,
$\triangle A E D \backsim \triangle A B C$,
$$
\begin{array}{c}
\frac{D E^{2}}{B C^{2}}=\frac{S_{\triangle A E D}}{S_{\triangle A B C}}=\frac{A D \cdot A E}{A B \cdot A C}=\cos ^{2} \alpha . \\
\therefore \quad \frac{D E}{B C}=|\cos \alpha| .
\end{array}
$$