Question

select the correct answer. which equation correctly solves the pythagorean theorem, (a^{2}+b^{2}=c^{2}), for (b), assuming (a), (b), and (c) are positive? a. (b = c - a) b. (b=sqrt{c^{2}-a^{2}}) c. (b=sqrt{c^{2}+a^{2}}) d. (b = c + a)

Explanation:

Step1: Isolate $b^{2}$ term

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 $b$ is positive, $b = \sqrt{c^{2}-a^{2}}$.

Answer:

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