Find the value of each variable. If your answer is NOT an integer, leave it in simplest radical form. Show work!!! Medal will be rewarded for patronage! :D

Question

firejay5 · Answer

|dw:1392253164418:dw|

firejay5 · Answer

@jdoe0001 @whpalmer4 @jim_thompson5910

whpalmer4 · Answer

are the two upper sides of equal length?

firejay5 · Answer

@whpalmer4 I am confused on your question

whpalmer4 · Answer

the triangle has 3 sides.  the bottom one is labeled $9\sqrt{2}$.  The right one is labeled $a$.  Is the left one of a known length?

firejay5 · Answer

no

whpalmer4 · Answer

Are you sure?  You can't figure it out from what you know about that triangle?  If you can't, I'm not sure you're going to have much luck with this problem unless you know trigonometry.

whpalmer4 · Answer

What kind of a triangle is that?

whpalmer4 · Answer

@firejay5 My 10 year old correctly identified that as an isosceles triangle and told me the length of the upper left side.  Maybe you should have another look, eh?

whpalmer4 · Answer

and now he's figured out $a$.  I had to remind him of the formula for the Pythagorean theorem, so I'll do the same for you:$$a^2+b^2=c^2$$$a,b$ are the lengths of the sides, $c$ is the length of the hypotenuse.  Don't tag me until you've gotten the correct answer here.

firejay5 · Answer

I got A = 9

whpalmer4 · Answer

Great!  Your tagging privileges are reinstated :-)

firejay5 · Answer

what do you mean by that?