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To solve for angle \( x \) in the given right triangle, we can use trigonometric functions. The sides provided are the opposite side (length \( 8 \)) and the adjacent side (length \( 6 \)) relative to angle \( x \).

### Step-by-Step Solution:

1. **Identify the trigonometric function to use:**
   - **Sine** function: \(\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}\)
   - **Cosine** function: \(\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
   - **Tangent** function: \(\tan(x) = \frac{\text{opposite}}{\text{adjacent}}\)

   Since you have the lengths of the opposite side (8) and the adjacent side (6), the appropriate function to use is **Tangent**.

2. **Apply the tangent function:**
   \[
   \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{6} = \frac{4}{3}
   \]

3. **Solve for \( x \):**
   \[
   x = \tan^{-1}\left(\frac{4}{3}\right)
   \]
   Using a calculator or trigonometric table:
   \[
   x \approx 53.13^\circ
   \]

### Answer:
The correct function to use is **C. Tangent**, and the value of \( x \) is approximately \( 53.13^\circ \).

Would you like more details on how to calculate the arctangent or have any other questions?

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**Related Questions:**

1. What are the exact values for sine and cosine of this angle \( x \)?
2. How would you solve for the hypotenuse using the given side lengths?
3. What is the relationship between sine, cosine, and tangent in a right triangle?
4. How can you verify the angle using the sine or cosine function?
5. How do you convert this angle from degrees to radians?

**Tip:** In trigonometry, it's important to always identify which sides of the triangle you are dealing with (opposite, adjacent, hypotenuse) before selecting a trigonometric function.

Solve for x in the right triangle with opposite side 8 and adjacent side 6. Which trigonometric function should you use?

Learn how to solve for the angle x in a right triangle with an opposite side of 8 and an adjacent side of 6. This problem demonstrates the use of the tangent function and inverse tangent to find the angle. Suitable for students in Grades 8-10.

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