The image shows two right triangles. To solve for $x$, we can apply the Pythagorean theorem twice, once for each triangle.

1. First triangle (the smaller one):

   • The legs are $x$ and $8$.
   • The hypotenuse is $10$.

   Using the Pythagorean theorem: $x^2 + 8^2 = 10^2$ Simplifying: $x^2 + 64 = 100$ $x^2 = 100 - 64 = 36$ $x = \sqrt{36} = 6$

The value of $x$ is 6.

Would you like further details or have any questions about the process? Here are some related questions to explore:

1. How can the Pythagorean theorem be applied to non-right triangles?
2. What is the geometric significance of simplifying radical expressions?
3. Can the Pythagorean theorem be extended to 3D shapes, like in three-dimensional space?
4. How would the answer change if one of the sides was a decimal or a radical number?
5. How does the concept of distance apply in the context of coordinate geometry?

Tip: Always check the conditions for applying the Pythagorean theorem, such as ensuring that you are working with a right triangle.