the pythagorean theorem, given by the formula ( a^{2}+b^{2}=c^{2} ), relates the three sides of a right…

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 ).

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 ).

Answer

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}})