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To find the length of side \( x \) in the right triangle, we can use the Pythagorean theorem, which states:

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

where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse. In this triangle, the hypotenuse is 8, one leg is 6, and we are looking for the length of the other leg, \( x \).

Rearranging the Pythagorean theorem to solve for \( x \), we have:

\[
x^2 = 8^2 - 6^2
\]

Calculating this, we find \( x \):

\[
x^2 = 64 - 36 = 28
\]
\[
x = \sqrt{28} \approx 5.29
\]

Thus, the length of side \( x \) is approximately 5.29, rounded to the nearest hundredth.

Would you like to know more about how this calculation works or have any other questions? Here are some related topics you might find interesting:

1. Can you explain why the Pythagorean theorem is applicable only to right triangles?
2. How do you find the area of this triangle?
3. What would the length of the hypotenuse be if the other two sides were different?
4. Can you show how the Pythagorean theorem is derived?
5. Are there any applications of the Pythagorean theorem in real life?

**Tip**: Remember that when using the Pythagorean theorem, always double-check that the triangle is a right triangle and that you are using the correct side as the hypotenuse, which is always the longest side.

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Learn how to find the missing side length of a right triangle using the Pythagorean theorem. Given one leg (6) and the hypotenuse (8), this step-by-step guide will help you solve for x, rounding the answer to the nearest hundredth.

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