3. Given that the base $BC$ and the height $AD$ of isosceles $\triangle ABC$ are both integers, then $\sin A$ and $\cos A$ are:
(A) one is a rational number, the other is an irrational number
(B) both are rational numbers
(C) both are irrational numbers
(D) whether they are rational or irrational depends on the values of $BC$ and $AD$
(B)
3. 【Analysis and Solution】In $\triangle A B C$, $A B=A C, A D \perp B C$ at $D$.
$$
\tan \frac{A}{2}=\frac{D C}{A D}=\frac{B C}{2 A D} \text {, }
$$

Since $B C$ and $A D$ are rational numbers,
$\therefore \tan \frac{A}{2}$ is a rational number.
And $\sin A=\frac{2 \tan \frac{A}{2}}{1+\tan ^{2} \frac{A}{2}}, \cos A=\frac{1-\tan ^{2} \frac{A}{2}}{1+\tan ^{2} \frac{A}{2}}$,
$\therefore \sin A, \cos A$ are both rational numbers. .