A 5.5m long ladder is leaned against a wall.

Let the distance between the wall and the foot of the ladder be $x \mathrm{~m}$

In right angled $\triangle A B C$, by using Pythagoras theorem, we get

$B C^{2}=A B^{2}+A C^{2}$

$\Rightarrow \quad(5.5)^{2}=x^{2}+(4.4)^{2}$

$\Rightarrow \quad x^{2}=(5.5)^{2}-(4.4)^{2}$

$\Rightarrow: \quad x^{2}=30.25-19.36$

$\Rightarrow \quad x^{2}=10.89$

$\Rightarrow \quad x=\sqrt{10.89}$

$\therefore \quad x=3.3 \mathrm{~m}$

Hence, the distance between the wall and the foot of the ladder is $3.3 \mathrm{~m}$.