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To find the length of the third side in the given right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse \( c \) is equal to the sum of the squares of the other two sides \( a \) and \( b \):

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

In this case, the given sides are 6 and 8. We need to determine if these are the legs (a and b) or if one of them is the hypotenuse (c).

Given that the right angle is between the sides 6 and 8, these are the legs of the triangle. Hence, we can calculate the hypotenuse \( c \) using:

\[ c^2 = 6^2 + 8^2 \]
\[ c^2 = 36 + 64 \]
\[ c^2 = 100 \]
\[ c = \sqrt{100} \]
\[ c = 10 \]

So, the length of the third side (the hypotenuse) is 10.

If you have any questions or want more details on the calculations, feel free to ask. Here are some related questions you might find interesting:

1. What is the Pythagorean theorem and how is it used?
2. How can you determine which side is the hypotenuse in a right triangle?
3. Can the Pythagorean theorem be used in non-right triangles?
4. How do you solve for a missing leg if the hypotenuse and one leg are known?
5. What are the real-world applications of the Pythagorean theorem?
6. How does the Pythagorean theorem relate to distance calculation in coordinate geometry?
7. Can the Pythagorean theorem be extended to three dimensions?
8. What are Pythagorean triples and how do they work?

**Tip:** When working with right triangles, always ensure to correctly identify the legs and the hypotenuse before applying the Pythagorean theorem.

Learn how to find the length of the hypotenuse in a right triangle using the Pythagorean theorem. Step-by-step solution provided for a triangle with legs of lengths 6 and 8. Suitable for students in Grades 7-9.

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