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The problem involves a right triangle with sides \( a = 6 \), \( b = 8 \), and the angle \( x \) corresponding to side \( b \). We are asked to find \( \cos(x) \).

### Step-by-step solution:

1. **Use the Pythagorean theorem** to find the hypotenuse \( c \):
   \[
   c = \sqrt{a^2 + b^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10
   \]

2. **Apply the cosine definition** for angle \( x \) in a right triangle:
   \[
   \cos(x) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{b}{c} = \frac{8}{10} = 0.8
   \]

Thus, \( \cos(x) = 0.8 \).

Let me know if you'd like more details or further explanations.

Here are some related questions:
1. How can we find \( \sin(x) \) for the same triangle?
2. What is \( \tan(x) \) in this triangle?
3. Can we find the angle \( x \) in degrees?
4. How does the Pythagorean theorem apply to non-right triangles?
5. What is the significance of cosine in trigonometry?

**Tip:** Always remember that cosine represents the ratio of the adjacent side to the hypotenuse in a right triangle.

In this right triangle, a = 6 and b = 8. It follows that cos(x) = ?

Learn how to calculate the cosine of angle x in a right triangle with sides a = 6 and b = 8. This problem covers key trigonometric concepts and the Pythagorean theorem, suitable for students in Grades 8-10.

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