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 a in terms of b and c.

Explanation:

Step1: Isolate $a^{2}$

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

Step2: Solve for $a$

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

Answer:

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