Question

82 in. 18 in. find the length of the missing side. 68 in. 20 in. 16 in. 80 in.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 82$ in and one - leg be $a = 18$ in. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the missing side. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 82$ and $a = 18$ into the formula: $b=\sqrt{82^{2}-18^{2}}=\sqrt{(82 + 18)(82 - 18)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{100\times64}$.

Step3: Calculate the square - root

$\sqrt{100\times64}=\sqrt{100}\times\sqrt{64}=10\times8 = 80$ in.

Answer:

80 in.