Question

given a right triangle with legs a and b and hypotenuse c, find the length of side b if c = 9, a = 7. answer: b =

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute given values

Substitute $c = 9$ and $a = 7$ into the formula. So $b=\sqrt{9^{2}-7^{2}}=\sqrt{81 - 49}=\sqrt{32}$.

Step3: Simplify the square - root

$\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$