The problem provided involves solving for the angle $x$ in a right triangle using the tangent function. We are given the following information:

$\tan(x) = \frac{6}{8}$

To solve for $x$, we need to use the inverse tangent function (also called arctangent), denoted as $\tan^{-1}$. The formula is:

$x = \tan^{-1}\left(\frac{6}{8}\right)$

Now, I'll calculate $x$ for you.The value of $x$ is approximately $36.87^\circ$ when rounded to the nearest hundredth.

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. How would you calculate the sine or cosine of angle $x$?
2. What are the other angles of this triangle if it is a right triangle?
3. How can you use the Pythagorean theorem to verify the triangle’s dimensions?
4. Can you solve for the angle if the tangent ratio was reversed, i.e., $\frac{8}{6}$?
5. How would you solve for the sides if you were given the angle instead of the sides?

Tip: Always use a scientific calculator or function when working with trigonometric functions for accurate results!