Sure, let's go through the steps to solve for [tex]\( c \)[/tex] in the equation [tex]\( c^2 = a^2 + b^2 \)[/tex], given specific values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
1. Identify the given values:
- [tex]\( a = 3 \)[/tex]
- [tex]\( b = 4 \)[/tex]
2. Plug the given values into the equation [tex]\( c^2 = a^2 + b^2 \)[/tex]:
[tex]\[
c^2 = 3^2 + 4^2
\][/tex]
3. Calculate the squares of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
[tex]\[
4^2 = 16
\][/tex]
4. Add the results of the squared values:
[tex]\[
c^2 = 9 + 16
\][/tex]
[tex]\[
c^2 = 25
\][/tex]
5. To find [tex]\( c \)[/tex], take the square root of both sides of the equation:
[tex]\[
c = \sqrt{25}
\][/tex]
6. Calculate the square root:
[tex]\[
c = 5
\][/tex]
So, the value of [tex]\( c \)[/tex] is [tex]\( 5 \)[/tex].
