Question

State what the length of the other leg is in a right triangle whose hypotenuse is 13 and one leg is 12 by using the Pythagorean Theorem.

Answer 1

6?

Answer 2

6 Is not correct. The pythagorean theorem says that \[c=\sqrt{a^2+b^2}\]correct?

Answer 3

Yes. I tried that and it doesn't come up with any of the multiple choice answers.

Answer 4

Let's rearrange it to find \(a\).\[\begin{aligned}
c&=\sqrt{a^2+b^2}\\
c^2&=a^2+b^2\\
c^2-b^2&=a^2\\
\sqrt{c^2-b^2}&=a
\end{aligned}\]

Answer 5

Now plug in \(13=c\), and \(12=b\). We get \[\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}\]So what's \(\sqrt{25}\)?

Answer 6

Is it simplified to 5? And the other leg.

Answer 7

Right. So the length of your third leg must be 5.

Answer 8

Thanks for the help.

Answer 9

No problem.