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To solve the problem of finding the missing side of this right triangle, we can apply the **Pythagorean Theorem**, which is used for right-angled triangles. The theorem is:

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

Where:
- \(c\) is the hypotenuse (the longest side, opposite the right angle),
- \(a\) and \(b\) are the other two sides.

In this triangle:
- The hypotenuse \(c = 13\),
- One leg \(a = 8\),
- We need to find the missing side \(b\).

Using the Pythagorean Theorem:

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

\[
64 + b^2 = 169
\]

\[
b^2 = 169 - 64
\]

\[
b^2 = 105
\]

Now, take the square root of both sides:

\[
b = \sqrt{105} \approx 10.25
\]

So, the missing side is approximately **10.25**.

Would you like any more details or clarifications on this solution?

Here are 5 related questions to deepen your understanding:
1. How does the Pythagorean Theorem work for larger triangles?
2. What are other ways to calculate the hypotenuse if both legs are known?
3. How would you find the area of this right triangle?
4. What are irrational numbers and why is the square root of 105 irrational?
5. Can the Pythagorean Theorem be applied to non-right triangles?

**Tip:** When using the Pythagorean Theorem, always double-check which side is the hypotenuse to avoid confusion in calculations!

Find the length of the missing side for this right triangle (Estimate an irrational answer to two decimal places).

Learn how to find the missing side of a right triangle using the Pythagorean Theorem. This problem involves calculating the side lengths of a triangle with sides of 8 and 13 using the equation a^2 + b^2 = c^2. Suitable for students in Grades 8-10.

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