The setup of both ladders will give us two triangles as shown below:
Since both triangles have 2 equal angles in both triangles, this means that they are both similar.
Hence, we can have a ratio of their sides equal to each other as follows:
[tex]\frac{|AC|}{|AB|}=\frac{|DF|}{|DE|}[/tex]
Substituting, we have
[tex]\begin{gathered} \frac{25}{35}=\frac{x}{14} \\ \therefore \\ x=\frac{25\times14}{35} \\ x=10\text{ ft} \end{gathered}[/tex]
The height is 10 feet.
