Let the height be h.
Then by Pythagorean rule, we have
[tex]h^2+5^2=13^2[/tex]Therefore,
[tex]\begin{gathered} h^2=13^2-5^2 \\ \Rightarrow h^2=169-25 \\ \Rightarrow h^2=144 \end{gathered}[/tex]Hence,
[tex]h=\sqrt[]{144}=12\text{ ft}[/tex]Hence the height is 12 feet
