x is the height of the ladder.
Two similar triangles are formed, then their corresponding sides satisfy the next proportion:
[tex]\frac{15\text{ ft}}{19\text{ ft}}=\frac{x\text{ ft}}{17\text{ ft}}[/tex]Solving for x,
[tex]\begin{gathered} 15\cdot17=x\cdot19 \\ \frac{255}{19}=x \\ 13.4\text{ ft = x} \end{gathered}[/tex]
