Question

1. ms. green tells you that a right triangle has a hypotenuse of 13 and a leg of 5. she asks you to find the other leg of the triangle. what is your answer?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Let one leg \(a = 5\), hypotenuse \(c=13\), and we need to find the other leg \(b\). Rearranging the formula for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values into the formula

Substitute \(a = 5\) and \(c = 13\) into the formula: \(b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}\).

Step3: Simplify the square root

\(\sqrt{144}=12\) since \(12\times12 = 144\).

Answer:

The length of the other leg is 12.