Question

find the value of b. pythagorean theorem: a² + b² = c² b = √?

Explanation:

Step1: Identify values for Pythagorean theorem

Let $a = 7$, $c=10$. Substitute into $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the formula to solve for $b^{2}$

$b^{2}=c^{2}-a^{2}$. Then $b^{2}=10^{2}-7^{2}$.

Step3: Calculate $10^{2}-7^{2}$

$10^{2}=100$, $7^{2} = 49$. So $b^{2}=100 - 49=51$.

Step4: Solve for $b$

$b=\sqrt{b^{2}}=\sqrt{51}$.

Answer:

$\sqrt{51}$