I don't understand the first two. I can't find the answer.  I think the last 4 are correct but I'm not sure. Please help!

mathelp  Aug 24, 2018

For the first two, you can use Pythagorean Theorem. This states that \({a}^{2}+{b}^{2}={c}^{2}\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. 


Problem 1: We already have sides \(a = 10\) and \(c = \sqrt{170}\). We can move the formula around for it to fit this problem better. We can change it to \({b}^{2}={c}^{2}-{a}^{2}\). When subsituting our values in, we can get \({b}^{2}={\sqrt{170}}^{2}-{10}^{2}\). When we square both values, we can get \({b}^{2} = 170-100\), so \({b}^{2} = 70\). We can solve this to be \(b = \sqrt{70}\) or \(x = \sqrt{70}\).


Problem 2: We already have sides \(b = 5\sqrt{2}\) and \(c = 13\). We can move the formula around for it to fit this problem better. We can change it to \({a}^{2}={c}^{2}-{b}^{2}\). When plugging in our values, we can get \({a}^{2} = {13}^{2} - ({5\sqrt{2})}^{2}\). By solving this, we can get \({a}^{2} = 119\) which equals \(a = \sqrt{119}\) or \(x = \sqrt{119}\).


- Daisy

dierdurst  Aug 24, 2018

Thank you so much for your help!! Are the last questions correct? I worked them out but I'm not 100% sure if they are right. Sorry.

mathelp  Aug 24, 2018

Guest, your last 4 answers are correct!

modus  Aug 24, 2018

Thank you!!

mathelp  Aug 24, 2018

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