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Find the value of each variable. If your answer is not an integer, express it in simplest radical form **check answer**

Mathematics
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Um... missing something?
should we get popcorn while you type in the variables?
yall patience is a virtue
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Other answers:

SOH CAH TOA
sounds like the tune of a hawaiian song, but that's all you need http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png
hmmm well, I see, you're using the 30-60-90 rule
well, hmm, still the 30-60-90 rule wouldn't end up using the sine function anyhow I mean you're given an angle's value, 30 degrees so I gather you're expected to use sine and cosine for that
otherwise, your answer will be in terms of "x" and "y"
hmm maybe not ...
in a 30-60-90 rule the smallest side, will half the longest that is "x" the smallest, is half 40 the longest and the OTHER side, is \(\bf \sqrt{3} \times \text{smallest side}\)
|dw:1375644053298:dw|
45-45-90 assumes you have 2 angles of 45 degrees you have there one of 30, and is a right triangle, so you have another of 90 and lastly one of 60
but yes, for the 45-45-90 rule, 2 sides are equal and the longest is \(\bf \sqrt{2}\) of either side
well, for that you'd need to use the \(\bf \sqrt{3}\) ratio for the longer side
|dw:1375644727216:dw|
http://upload.wikimedia.org/wikipedia/commons/4/45/30-60-90_triangle.jpg
those are the ratio relationships on a triangle with 30-60-90 angles if I were to stand up yours, it'd look like |dw:1375645193671:dw|
so, what part confuses? in a 30-60-90 rule, each side have a ratio relationship, as shown above
ok
so you want to know what "x" is in the triangle notice that the triangle has a hypotenuse of 40 and 2 angles, a 30 degrees one and a 90 degrees one the other internal angle has to be a 60 degrees one so that makes it a 30-60-90 triangle, whose side relationships are well known
i reposted it that way we wouldnt have all the ^^ in the way

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