Question

1. can you identify each missing side as a leg or a hypotenuse? leg or hypotenuse? 48 80 x

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the legs. Here, assume the legs are \(x\) and \(48\), and the hypotenuse is \(80\).

Step2: Apply the Pythagorean theorem

We have \(x^{2}+48^{2}=80^{2}\), which can be rewritten as \(x^{2}=80^{2}-48^{2}\).

Step3: Calculate the squares

\(80^{2}=6400\) and \(48^{2}=2304\). So \(x^{2}=6400 - 2304=4096\).

Step4: Find the value of \(x\)

Take the square - root of both sides. Since \(x\) represents the length of a side of a triangle, we take the positive square - root. \(x=\sqrt{4096}=64\). And \(x\) is a leg of the right - triangle.

Answer:

The missing side \(x = 64\) and it is a leg.