https://file.aiquickdraw.com/mathbot/file/1727225580032votgd9wm.jpg

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.

Solve for x. Leave your answer in simplest radical form. (The image shows two right triangles. One triangle has legs of x and 8, and the hypotenuse is 10. The other triangle has legs 7 and 10.)

This problem involves solving for x in a right triangle using the Pythagorean theorem. One triangle has sides x, 8, and 10. Learn how to apply the theorem and simplify the answer in radical form.

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