To solve for [tex]\( c \)[/tex] using the Pythagorean theorem, we need to follow these steps:
1. Understand the theorem: According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is expressed as:
[tex]\[
a^2 + b^2 = c^2
\][/tex]
2. Input the given values: To proceed, we need to have specific values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. Since they are not provided here, we will use variables to represent these lengths.
3. Apply the theorem: Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the equation:
[tex]\[
a^2 + b^2 = c^2
\][/tex]
4. Solve for [tex]\( c^2 \)[/tex]:
[tex]\[
c^2 = a^2 + b^2
\][/tex]
5. Find [tex]\( c \)[/tex]: To solve for [tex]\( c \)[/tex], we need to take the square root of both sides of the equation:
[tex]\[
c = \sqrt{a^2 + b^2}
\][/tex]
6. Final solution: The final solution for [tex]\( c \)[/tex] is:
[tex]\[
c = \sqrt{a^2 + b^2}
\][/tex]
Thus, [tex]\( c \)[/tex] can be determined by taking the square root of the sum of the squares of [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
