Question

use the pythagorean theorem to find the missing leg of the triangle below. (there is a right triangle image with one leg labeled 5, hypotenuse labeled 13, and the right angle marked.)

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let the missing leg be \(x\), one leg \(a = 5\), hypotenuse \(c=13\). So \(5^{2}+x^{2}=13^{2}\).

Step2: Solve for \(x^{2}\)

Calculate \(5^{2}=25\), \(13^{2} = 169\). Then \(x^{2}=169 - 25=144\).

Step3: Find \(x\)

Take square root of \(144\), \(x=\sqrt{144} = 12\).

Answer:

12