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 $AD$.


3. (B)
$$
\begin{array}{c}
\triangle A B C \text { where } A B=A C, A D \perp B C \text { at } D . \\
\operatorname{tg} \frac{A}{2}=\frac{D C}{A D}=\frac{B C}{2 A D}
\end{array}
$$

Since $B C$ and $A D$ are rational numbers,
$\therefore \operatorname{tg} \frac{A}{2}$ is a rational number.
$$
\text { and } \begin{aligned}
\sin A & =\frac{2 \operatorname{tg} \frac{A}{2}}{1+\operatorname{tg}^{2} \frac{A}{2}}, \\
\cos A & =\frac{1-\operatorname{tg}^{2} \frac{A}{2}}{1+\operatorname{tg}^{2} \frac{A}{2}}
\end{aligned}
$$
$\therefore \sin A, \cos A$ are both rational numbers.