The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]
Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]
Then, the ladder reach 12 feet up the side of the house
