Question

what is the formula used to solve for the hypotenuse?

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, for legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\).

Step2: Analyze other options

• For \(c - a=c\), simplifying gives \(-a = 0\) (not a valid general formula for right - triangles).
• For \(a + b=c\), by triangle inequality in a non - degenerate triangle \(a + b>c\) (and in a right - triangle, this is not the formula for the hypotenuse).
• For \(a - b=c\), since \(a,b,c>0\) (side lengths) and \(a>b\) (assuming \(a\) is a longer leg), \(a - b

Answer:

\(a^{2}+b^{2}=c^{2}\)