Let's begin by listing out the information given to us:
There are 2 triangles in the picture:
[tex]\begin{gathered} h_1=h,h_2=6\frac{1}{2}ft=\frac{13}{2}ft,b_1=31\frac{1}{2}ft=\frac{63}{2}ft,b_2=9ft \\ h\colon\frac{13}{2}=\frac{63}{2}\colon9\Rightarrow\frac{h}{\frac{13}{2}}=\frac{63}{2\cdot9}\Rightarrow\frac{2h}{13}=\frac{63}{2\cdot9} \\ 2h=\frac{63\cdot13}{2\cdot9}\Rightarrow2h=\frac{7\cdot13}{2} \\ h=\frac{7\cdot13}{2\cdot2}=\frac{91}{4} \\ h=22\frac{3}{4}ft \end{gathered}[/tex]
