hello
to slve this question, we need to draw a diagram to illustrate the situation
this would give us a better insight to solve the problem
to solve this question, we would use pythagorean theorem
[tex]\begin{gathered} \text{hyp}^2=\text{adj}^2+\text{opp}^2 \\ \text{hypothen }=10 \\ \text{adjacent}=5 \\ \text{opposite}=y \end{gathered}[/tex]
this can be rewritten as
[tex]\begin{gathered} x^2=y^2+z^2 \\ x=10 \\ z=5 \\ 10^2=y^2+5^2 \\ 100=y^2+25 \\ \text{collect like terms} \\ y^2=100-25 \\ y^2=75 \\ \text{take the square root of both sides} \\ y=\sqrt[]{75} \\ y=8.66\approx8.7ft \end{gathered}[/tex]
the height at which the ladder touches the wall of the house is at 8.7ft
