Step 1: Identify the relevant sides for the tangent function
The tangent of an angle in a right-angled triangle is defined as the ratio of the side opposite the angle to the side adjacent to the angle. In this case, the angle is $x^\circ$. The side opposite to $x^\circ$ is $f$, and the side adjacent to $x^\circ$ is $e$.
Step 2: Write the tangent of the angle x
Using the definition of the tangent function, we can write:
$\tan x^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{f}{e}$.