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 $BD$ and $AC$
Given $A B=c, B C=a, A D=h \Rightarrow c^{2}=\frac{a^{2}}{4}+h^{2}$, and $\sin \frac{A}{2}=\frac{a}{2 c}, \cos \frac{A}{2}=\frac{h}{c}$. Therefore, $\sin A=\frac{a h}{2^{2}}, \cos A=\frac{4 h^{2}-a^{2}}{4^{2}}$ are both rational numbers, so the answer is $B$.