Question

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 $b^{2}$

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

Step2: Solve for $b$

Since $b>0$, take the square - root of both sides. So $b = \sqrt{c^{2}-a^{2}}$.

Answer:

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