Question

square roots and right triangles
which equation could be used to find the length of the hypotenuse?
$5^{2}+8^{2}=c^{2}$
$5^{2}+c^{2}=8^{2}$
$c^{2}-5^{2}=8^{2}$
$8^{2}-5^{2}=c^{2}$

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Identify legs and hypotenuse

In \(\triangle ABC\), \(a = 5\) (one leg), \(b = 8\) (another leg), and \(c\) is the hypotenuse.
Substitute \(a = 5\) and \(b = 8\) into the Pythagorean theorem: \(5^{2}+8^{2}=c^{2}\).

Answer:

\(5^{2}+8^{2}=c^{2}\)