Question

an alternative form of the pythagorean theorem, $c^{2}-b^{2}>a^{2}$, can be used to find the length of one can be determined if the lengths of the hypotenuse and the other leg are known. the converse of the pythagorean theorem helps to verify if a triangle is -angled.

Explanation:

The Pythagorean Theorem \(c^{2}=a^{2}+b^{2}\) (where \(c\) is the hypotenuse of a right - angled triangle and \(a\) and \(b\) are the legs). The formula \(c^{2}-b^{2}=a^{2}\) (derived from the Pythagorean Theorem by subtracting \(b^{2}\) from both sides) is used to find the length of a leg (\(a\) or \(b\)) when the hypotenuse (\(c\)) and the other leg are known.

The converse of the Pythagorean Theorem states that if \(a^{2}+b^{2}=c^{2}\) for a triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), then the triangle is right - angled.

Answer:

1. leg
2. right