Let's construct the given data as a right angled triangle since wall of the house and the base will be perpendicular to each other.
Using Pythagoras theorem
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ 10^2=x^2+5^2 \\ 100=x^2+25 \\ x^2=100-25 \\ x^2=75 \\ x=\sqrt[]{75} \\ x=\sqrt[]{5\times5\times3} \\ x=5\sqrt[]{3} \end{gathered}[/tex]Hence the height of the wall, that ladder touches is,
[tex]5\sqrt[]{3}[/tex]
