11We are given a problem that can be exemplified in the following diagram:
Since the ladder, the wall and the floor form a right triangle we can use the Pythagorean theorem:
[tex]h^{2^{}}=a^2+b^2[/tex]Where
[tex]\begin{gathered} h=\text{hypotenuse} \\ a=\text{height} \\ b=x \end{gathered}[/tex]In this case, the hypotenuse is the length of the ladder and the height is the height of the window. Replacing the known values:
[tex](20)^2=(18)^2+b^2[/tex]Solving the square:
[tex]400=325+b^2[/tex]Now we solve for "b", first by subtracting 325 to both sides:
[tex]400-325=b^2[/tex]Solving the operation:
[tex]75=b^2[/tex]Taking square root to both sides:
[tex]\sqrt[]{75}=b[/tex]Solving the square root:
[tex]8.7=b[/tex]Therefore, the foot of the ladder is 8.7 feet from the building.
