Answer
$27.50 \ \mathrm{ft}$
Work Step by Step
Draw a diagram of the problem like the one shown below and find the height that the ladder will reach when placed $12$ feet from the base of the house. Let $y$ be the wall's height. We use the Pythagorean theorem to find the height of the wall:
$$
\begin{aligned}
y^2+12^2 & =30^2 \\
y^2 & =30^2-12^2 \\
y^2 & =900-144 \\
y^2 & =756 \\
y & =\pm\sqrt{756} \\
y&=\sqrt{756}\\
&\approx 27.50 \ \mathrm{ft}.
\end{aligned}
$$ We took only the positive value since the height of the wall must be positive.
The required height is about $27.50 \ \mathrm{ft}$.
