Let's first get a sketch that represents this situation.
Here,
L represents the laddder
B represents the building
F represents the floor(distance between the base of the ladder and the building).
We have the equation, use pythagoras theorem:
[tex]l^2=b^2^{}+f^2[/tex]To find the distance between the base of the ladder and the building, rewrite the formula above for f.
Thus, we have:
[tex]\begin{gathered} f^2=l^2-b^2 \\ \\ f=\sqrt[]{l^2-b^2} \end{gathered}[/tex]