Question

find the length of the missing side. 20 in. 16 in. 68 in. 80 in.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 82$ in and one - leg $a = 18$ in. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

$b^{2}=82^{2}-18^{2}=(82 + 18)(82 - 18)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).
$b^{2}=(100)(64)$.

Step3: Calculate $b$

$b^{2}=6400$, then $b=\sqrt{6400}=80$ in.

Answer:

80 in.