Question

1. the pythagorean theorem, given by the formula $a^{2}+b^{2}=c^{2}$, relates the three sides of a right triangle. solve the formula for the positive value of c in terms of a and b.

Explanation:

Step1: Isolate $c^{2}$

Given $a^{2}+b^{2}=c^{2}$, $c^{2}$ is already isolated.

Step2: Solve for $c$

Take the square - root of both sides. Since we want the positive value of $c$, we have $c = \sqrt{a^{2}+b^{2}}$.

Answer:

$c=\sqrt{a^{2}+b^{2}}$