Question

find the length of the missing side.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 82$ in and one - side be $a = 18$ in. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, 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 $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate

First, $(82 + 18)(82 - 18)=100\times64 = 6400$. Then $\sqrt{6400}=80$ in.

Answer:

80 in.