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To find the value of \( x \) using the Pythagorean Theorem, we apply the formula:

\[
a^2 + b^2 = c^2
\]

In this case, \( a = 8 \), \( c = 13 \), and we are solving for \( b = x \).

Thus, the equation becomes:

\[
8^2 + x^2 = 13^2
\]

Now, let me solve for \( x \).The value of \( x \) is approximately 10.25. Since this value is not among the answer choices, it seems there might be a discrepancy. Could you confirm if this is what you expected, or would you like further clarification?

Here are some questions for further practice:

1. How would you modify the equation if you were solving for a different side of the triangle?
2. What happens if the triangle's hypotenuse is unknown and you need to solve for it?
3. Can you explain why the Pythagorean theorem only applies to right-angled triangles?
4. How does this equation change in three-dimensional geometry?
5. What would the Pythagorean theorem look like if we changed the numbers involved?

**Tip**: Always ensure your measurements and units are consistent when solving geometric problems.

Using the Pythagorean Theorem, find the value of x for a right-angled triangle with side lengths 8 and 13.

Learn how to solve for x in a right-angled triangle using the Pythagorean Theorem with side lengths 8 and 13. This step-by-step solution includes key geometric concepts and a detailed explanation of the formula a^2 + b^2 = c^2. Suitable for Grades 7-10.

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