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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!

Solve for x: Use the inverse tangent function (tan^(-1)(6/8)) to find the value of angle x in a right triangle where the opposite side is 6 and the adjacent side is 8.

Learn how to find the angle x in a right triangle using the inverse tangent function, given the opposite and adjacent sides. This problem demonstrates key trigonometric concepts and calculations, suitable for high school students in Grades 9-12.

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