Answer
$20.67 \ ft$
Work Step by Step
The trigonometric functions can be expressed as:
$\sin \theta=\dfrac{Opposite}{Hypotenuse} \\ \cos \theta=\dfrac{Adjacent}{Hypotenuse} \\ \tan \theta=\dfrac{Opposite}{Adjacent}$
We are given the angle and hypotenuse. Our aim is to compute the opposite side. So we use sine.
Let $a$ be the height of the ladder that touches the building and consider it as a opposite side.
Since, $\sin \theta=\dfrac{Opposite}{Hypotenuse}$
Therefore, $\sin (70^{\circ})=\dfrac{a}{22} \implies a \approx 20.67 \ ft$
