he Pythagorean Theorem: $$ a^{2}+b^{2}=c $$ $$ 84^{2}+8 \dot{0}^{2}=c^{2} $$ Solve for $$ c $$

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Given the Pythagorean Theorem: $$ a^{2}+b^{2}=c^{2} $$, we are provided with the values of $$ a = 84 $$ and $$ b = 80 $$. We need to solve for $$ c $$.

Substitute the values of $$ a $$ and $$ b $$ into the Pythagorean Theorem equation:

$$ 84^{2} + 80^{2} = c^{2} $$

Now, we can calculate the value of $$ c $$ by finding the square root of the sum of the squares of $$ a $$ and $$ b $$.

Let's calculate this:
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{84^{2}+80^{2}}$$
- step1: Add the numbers:
  $$\sqrt{13456}$$
- step2: Write in exponential form:
  $$\sqrt{116^{2}}$$
- step3: Simplify the root:
  $$116$$
The value of $$ c $$ is 116.
The value of $$ c $$ is 116.

he Pythagorean Theorem:

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