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 $AD$.
Answer ( )
In $\triangle ABC$, $AB = AC$, $AD \perp BC$ at $D$.
$$
\operatorname{tg} \frac{A}{2} = \frac{DC}{AD} = \frac{BC}{2AD},
$$

Since $BC$ and $AD$ are rational numbers,
$\therefore \operatorname{tg} \frac{A}{2}$ is a rational number.
And $\sin A = \frac{2 \operatorname{tg} \frac{A}{2}}{1 + \operatorname{tg}^2 \frac{A}{2}}$,
$$
\cos A = \frac{1 - \operatorname{tg}^2 \frac{A}{2}}{1 + \operatorname{tg}^2 \frac{A}{2}},
$$
$\therefore \quad \sin A, \cos A$ are both rational numbers.