[ The larger side is opposite the larger angle ]

The base $D$ of the height $A D$ of triangle $A B C$ lies on side $B C$, and $\angle B A D > \angle C A D$. Which is larger, $A B$ or $A C ?$
If $\angle B A D > \angle C A D$, then $\angle A B C \angle C A D$, then

$$
\angle A B C = 90^{\circ} - \angle B A D A C$.

## Answer

$A B > A C$.