To solve this problem, we use the Pythagorean Theorem, which states:

$a^2 + b^2 = c^2$

Here, $a$ and $b$ are the legs of the right triangle, and $c$ is the hypotenuse (the longest side opposite the right angle).

Given:

• One leg $a = 6$
• Another leg $b = 8$

We need to find $c$, the hypotenuse.

Step 1: Apply the formula

$c^2 = a^2 + b^2$ $c^2 = 6^2 + 8^2$ $c^2 = 36 + 64$ $c^2 = 100$

Step 2: Solve for $c$

$c = \sqrt{100} = 10$

Final Answer:

The length of the third side (the hypotenuse) is 10.0.

Would you like additional details or explanations?

Here are 5 related questions to deepen your understanding:

1. What is the Pythagorean Theorem, and why does it only apply to right triangles?
2. How would the problem change if you were solving for one of the legs instead of the hypotenuse?
3. How do you determine which side is the hypotenuse in any right triangle?
4. Can you calculate the area of this triangle using the two given legs?
5. How can the Pythagorean Theorem be applied in 3D problems?

Tip: Always check if a triangle is a right triangle before applying the Pythagorean Theorem. Look for a 90-degree angle!