Example 1 As shown in Figure 1, two utility poles $A B$ and $C D$ are erected on a construction site. They are $15 \mathrm{~m}$ apart, and points $A$ and $C$ are $4 \mathrm{~m}$ and $6 \mathrm{~m}$ above the ground, respectively. Steel wires are stretched from these points to points $E$ and $D$, and $B$ and $F$ on the ground to secure the poles. The height of the intersection point $P$ of the steel wires $A D$ and $B C$ above the ground is $\qquad$ $\mathrm{m}$.
(2000, National Junior High School Mathematics Competition)
As shown in Figure 1, draw $P H \perp B D$ at point $H$. Then
$A B / / P H / / C D$.
From $\triangle D P H \backsim \triangle D A B \Rightarrow \frac{P H}{A B}=\frac{D H}{B D}$;
From $\triangle B P H \backsim \triangle B C D \Rightarrow \frac{P H}{C D}=\frac{B H}{B D}$.

Adding the two equations yields $\frac{1}{A B}+\frac{1}{C D}=\frac{1}{P H}$.
Therefore, $P H=\frac{12}{5}$.