If a tree has a height of 186 feet, what is the angle of elevation from level ground measured from 57 feet away? Round your answer to the nearest tenth of a degree.

We start by considering a right triangle where the tree forms the opposite side and the horizontal distance from the tree forms the adjacent side. The angle of elevation, denoted by [tex]$\theta$[/tex], can be determined using the tangent function:

[tex]$$
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
$$[/tex]

Since the tree is [tex]$186$[/tex] feet tall (opposite side) and the distance is [tex]$57$[/tex] feet (adjacent side), we compute:

[tex]$$
\tan \theta = \frac{186}{57} \approx 3.2632
$$[/tex]

To find the angle [tex]$\theta$[/tex], we take the inverse tangent (arctan) of this ratio:

[tex]$$
\theta = \arctan(3.2632)
$$[/tex]

Evaluating [tex]$\arctan(3.2632)$[/tex], we obtain:

[tex]$$
\theta \approx 1.2734 \text{ radians}
$$[/tex]

Since the answer needs to be in degrees, we convert from radians to degrees using the conversion factor [tex]$180^\circ/\pi$[/tex]:

[tex]$$
\theta \approx 1.2734 \times \frac{180^\circ}{\pi} \approx 72.9622^\circ
$$[/tex]

Finally, rounding the result to the nearest tenth of a degree gives:

[tex]$$
\theta \approx 73.0^\circ
$$[/tex]

Thus, the angle of elevation from level ground measured from [tex]$57$[/tex] feet away is approximately [tex]$\boxed{73.0^\circ}$[/tex].