## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$14.03^{\circ}$
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 opposite side and adjacent side. Our aim is to compute the the angle. So we use Tangent. Let $a$ be the height of the ladder that touches the building and consider it as the opposite side. Since, $\tan \theta=\dfrac{Opposite}{Adjacent}$ Therefore, $\tan \theta=\dfrac{3}{12} \implies \theta =\arctan (\dfrac{3}{12})$ or, $\theta \approx 14.03^{\circ}$