To find the missing side using the Pythagorean Theorem, we need to remember the theorem itself, which states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), the relationship is given by:
\[ a^2 + b^2 = c^2 \]
Let's analyze each option:
Option A: \( x^2 + (10)^2 = 8^2 \)
Here, you are trying to solve for \( x \), assuming 10 is one leg and 8 is the hypotenuse. However, 8 should not be the hypotenuse since it's less than 10. This is incorrect.
Option B: \( x + 8 = 10 \)
This is not using the Pythagorean theorem since it's not in the form of \( a^2 + b^2 = c^2 \). This is simply a linear equation. Thus, this is incorrect.
Option C: \( x^2 + 8^2 = (10)^2 \)
This correctly sets up the equation based on the Pythagorean theorem. Here, if we consider 10 as the hypotenuse and 8 as one of the legs, this makes sense. This option is valid.
Option D: \( 8^2 + (10)^2 = x^2 \)
This does not follow the Pythagorean theorem. In this case, one side cannot be greater than the hypotenuse. This option is also incorrect.
Given the options:
- C is the correct usage of the Pythagorean Theorem to find the missing side, where \( x^2 + 8^2 = 10^2 \).