When you have two triangles as given, they are similar triangles. It means that the ratio between corresponding sides is the same.
Corresponding sides are:
Side x (height of the wall) and the height of the person (6 feet)
Distance between the wall and the foot of the lader (6 feet + 9 feet= 15 feet) and distance between the person and the foot of the lader (6 feet)
Then, you have the next:
[tex]\frac{x}{6ft}=\frac{15ft}{6ft}[/tex]
Solve for x:
[tex]\begin{gathered} x=6ft\cdot\frac{15ft}{6ft} \\ \\ x=15ft \end{gathered}[/tex]Then, the height of the wall is 15 feet
