Question

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 $b$ in terms of $a$ and $c$.

Explanation:

Step1: Isolate $b^{2}$

Subtract $a^{2}$ from both sides of the equation $a^{2}+b^{2}=c^{2}$.
$b^{2}=c^{2}-a^{2}$

Step2: Solve for $b$

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

Answer:

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