Answer
$20.40\ \mathrm{ft}$
Work Step by Step
Draw a diagram of the problem like the one shown below and note by $x$ the distance that the ladder will placed from the base of the house. Use the Pythagorean Theorem to find $x$:
$$
\begin{aligned}
x^2+22^2 & =30^2 \\
x^2 & =30^2-22^2 \\
x^2 & =900-484 \\
x^2 & =416 \\
x & =\pm \sqrt{416} \\
x&=\sqrt{416}\\
& \approx 20.40 \text{ ft}.
\end{aligned}
$$ We took only the positive value since the distance must be positive.
The required distance is about $20.40\ \mathrm{ft}$.
