The awning is the hypotenuse (5 ft). The horizontal extension is 2 ft (adjacent to $\theta$). The vertical drop $= \sqrt{25 - 4} = \sqrt{21}$.

The angle $\theta$ is between the building (vertical) and the awning. The side adjacent to $\theta$ along the building is $\sqrt{21}$, and the side opposite $\theta$ is $2$.

$\cos\theta = \frac{2}{5}$

So $\theta = \cos^{-1}\!\left(\frac{2}{5}\right)$. But let me check: $\theta$ is at the top where the awning meets the building. Adjacent = 2 (horizontal), hypotenuse = 5.

$\theta = \sin^{-1}\!\left(\frac{2}{5}\right)$

Actually, $\theta$ is between the building and the awning. The building is vertical, the awning goes out at angle $\theta$ from vertical. The horizontal distance (opposite to $\theta$) is 2, hypotenuse is 5.

$\sin\theta = \frac{2}{5}, \quad \theta = \sin^{-1}\!\left(\frac{2}{5}\right)$