Question

find the value of a. 7 in 12 in a =? pythagorean theorem a² + b² = c²

Explanation:

Step1: Identify Pythagorean theorem components

In a right - triangle, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $b = 7$ in and $c=12$ in, and we need to find $a$.

Step2: Rearrange the Pythagorean theorem

We can rewrite the formula as $a=\sqrt{c^{2}-b^{2}}$.

Step3: Substitute values

$a=\sqrt{12^{2}-7^{2}}=\sqrt{144 - 49}=\sqrt{95}\approx9.75$ in.

Answer:

$\sqrt{95}\text{ in}\approx9.75\text{ in}$