15. As shown in Figure 5, there is an iron tower $A B$ at the top of a slope. Under the sunlight, the tower's shadow $D E$ is cast on the slope. It is known that the base width of the tower $C D=14 \mathrm{~m}$, the length of the tower's shadow $D E=36 \mathrm{~m}$, and both Xiao Ming and Xiao Hua are $1.6 \mathrm{~m}$ tall. Xiao Ming stands at point $E$, and his shadow is also on the slope, while Xiao Hua stands at the foot of the slope along the direction of $D E$, and his shadow is on the flat ground. The lengths of their shadows are $4 \mathrm{~m}$ and $2 \mathrm{~m}$, respectively. Therefore, the height of the tower $A B=$ $\qquad$ $\mathrm{m}$.
15.20.

Draw a perpendicular from point $D$ to $CD$ intersecting $AE$ at point $F$, and draw a perpendicular from point $F$ to $AB$, with the foot of the perpendicular being $G$. It is easy to see that
$$
\begin{array}{l}
D F=\frac{1.6}{4} D E=14.4(\mathrm{~m}), \\
A G=\frac{1.6}{2} F G=\frac{1.6}{2} B D=5.6(\mathrm{~m}) .
\end{array}
$$

Therefore, $A B=A G+B G=A G+D F=20(\mathrm{~m})$.