Problem

missing length.
\[
c=\sqrt{[?]}
\]
Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$
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Answer

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Answer

\(\boxed{c = \sqrt{a^2 + b^2}}\)

Steps

Step 1 :Given the Pythagorean Theorem: \(a^2 + b^2 = c^2\)

Step 2 :We are asked to find the missing length \(c\), so we need to solve for \(c\) in the equation.

Step 3 :Rearrange the equation to isolate \(c\): \(c = \sqrt{a^2 + b^2}\)

Step 4 :Now, we can plug in the given values of \(a\) and \(b\) to find the missing length \(c\).

Step 5 :Finally, we get \(c = \sqrt{a^2 + b^2}\) as the expression for the missing length.

Step 6 :\(\boxed{c = \sqrt{a^2 + b^2}}\)

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