3. In Rt $\triangle A B C$, $\angle B=90^{\circ}, A B=15, B C=20$. Then the number of line segments with integer lengths connecting vertex $B$ to points on the hypotenuse (including sides $A B, B C$) is
A. 9
B. 10
C. 11
D. 12
In $\triangle A B C$, the altitude $B H=12$. From vertex $A$, line segments of lengths 13 and 14 can be drawn. From vertex $C$, line segments of lengths 13, 14, 15, 16, 17, 18, and 19 can be drawn. Therefore, the number of line segments with integer lengths is $2+7+3=12$, so the answer is $D$.