A tree casts a shadow as shown in the image. If the tree is 34 feet tall, and the distance from the top of the tree to the top of the shadow is 47 feet, what is the angle formed from the top of the tree? Round your answer to the nearest whole degree.
Let's call the angle formed by the top of the tree as angle $A$. Since we want to find the angle to the nearest whole degree, we can round our answer at the end.
Because $\angle A$ is an angle, we have that $\angle A$ is between $0^\circ$ and $180^\circ$.
Using the shadow as our reference, we start by realizing that the height of the tree is equivalent to the height of the shadow plus the distance from the top of the shadow to the top of the tree.
$\text{Tree height} = \text{Shadow height} + \text{Distance from top of the shadow to top of the tree}$
Since the tree is $34$ feet tall, the shadow's height is $34 - 47 = -13$ feet (a negative height does not make sense physically). Therefore, the top of the shadow is $13$ feet below the top of the tree, and the height of the shadow is $13$ feet.
The tangent of $\angle A$ is equal to the ratio between the height of the shadow and the distance of the top of the tree to the top of the shadow. So, $\tan A = \frac{13}{47}$.
If we take the arctangent of both sides of the equation, we get $A = \arctan\left(\frac{13}{47}\right)$.
Using a calculator, we find that $A \approx 15.15^\circ$.
Thus, the angle formed from the top of the tree is $\boxed{15^\circ}$, rounded to the nearest degree.