Question

level 3 find the length of the missing side. 82 in. 18 in. 80 in. 16 in. 20 in. 68 in.

Explanation:

Step1: Apply Pythagorean theorem

Let the missing side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 82\) (hypotenuse) and \(b=18\). So \(x^{2}+18^{2}=82^{2}\).

Step2: Rearrange the formula to solve for \(x\)

\(x^{2}=82^{2}-18^{2}\). Using the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), here \(a = 82\), \(b = 18\). Then \(x^{2}=(82 + 18)(82-18)=(100)\times(64)\).

Step3: Calculate \(x\)

\(x^{2}=6400\), so \(x=\sqrt{6400}=80\).

Answer:

\(80\) in.