13.095. On a flat horizontal platform, two masts stand 5 m apart from each other. At a height of $3.6 \mathrm{M}$ above the platform, one end of a wire segment $13 \mathrm{M}$ long is attached to each mast. The wire is stretched in the plane of the masts and is attached to the platform, as shown in Fig. 13.7. At what distance from the nearest mast is the point where the wire is attached to the platform?
Solution.

Let the required distance be $x$. From $\triangle A B C$ we get:

$A B^{2}+B C^{2}=A C^{2} ; A C=y,(x+5)^{2}+3.6^{2}=y^{2}$. From $\triangle A E D$ we get:

$A E^{2}+E D^{2}=A D^{2} ; A D=z \cdot x^{2}+3.6^{2}=z^{2}$. According to the condition: $z+y=13$. Solving the system: $\left\{\begin{array}{l}(x+5)^{2}+3.6^{2}=y^{2}, \\ x^{2}+3.6^{2}=z^{2}, \\ z+y=13,\end{array}\right.$ we find that $x=2.7$ m.

Answer: $2.7 \mathrm{~m}$.