13. As shown in Figure 6, Building A is $16 \mathrm{~m}$ tall, and Building B is located directly north of Building A. It is known that the angle between the sun's rays and the horizontal plane at noon on the winter solstice is $30^{\circ}$. At this time, find:
(1) If the distance between the two buildings is $20 \mathrm{~m}$, how high does the shadow of Building A fall on Building B?
(2) If the shadow of Building A just does not fall on Building B, what should be the distance between the two buildings?
Three, 13. (1) Suppose that when the sun is at its lowest in winter, the shadow of point $A$, the highest point of Building A, falls on point $C$ of Building B. Then, the length of $C D$ is the height of Building A's shadow on Building B.
Let $C E \perp A B$ at point $E$. In $\triangle A E C$,
$$
\angle A E C=90^{\circ}, \angle A C E=30^{\circ}, E C=20 \mathrm{~m} \text {. }
$$

Therefore, $A E=E C \cdot \tan \angle A C E=20 \times \frac{\sqrt{3}}{3}$
$$
\approx 11.6(\mathrm{~m}) . \\
C D=E B=A B-A E=4.4(\mathrm{~m}) .
$$
(2) Suppose the shadow of point $A$ falls on a point $F$ on the ground, then in $\triangle A B F$, $\angle A F B=30^{\circ}, A B=16 \mathrm{~m}$. Therefore,
$$
B F=A B \cdot \cot \angle A F B=16 \times \sqrt{3} \approx 27.7(\mathrm{~m}) .
$$

Thus, for the shadow of Building A to just not fall on Building B, the distance between the two buildings should be at least $27.7 \mathrm{~m}$.