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 \(b^{2}\)

Given \(a^{2}+b^{2}=c^{2}\), subtract \(a^{2}\) from both sides:
\(b^{2}=c^{2}-a^{2}\)

Step2: Solve for \(b\)

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

Answer:

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