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

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Do you know your trig functions? Like what sin, cos, tan are in regards to a triangle?
nope not really

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Ah. Alright, hang on then :P Keep in mind as I write these out, they are all in reference to the angle you are using.
that helps alot :DD
\[\sin = \frac{ opposite side }{ hypotenuse }\] \[\cos = \frac{ adjacent side }{ hypotenuse }\] \[\tan = \frac{ opposite side }{ adjacent side }\] People are ususally taught Soh Cah Toa as a way to remember which sides the trig functions refer to. Now again, these are in reference to your angle, so I'll draw that real quick.
That kind of make sense so far?
so far yes
Okay, cool. So this is your triangle that we have then: |dw:1375810542321:dw|
In order to solve this, we need to choose an angle (not the right angle) and then an appropriate trig function, sin, cos, or tan. The one we choose must include the side we know, 10 in this case, and then the value we want to find. that make sense?
im not entirely sure how to use them though
Right, we're getting to that :P I just wanted to see if you were following me so far.
oh well yes im following ya
Okay, cool. So next part: Let's say to find x I choose the 60 degree angle. Now in reference to the 60 degree angle, x is on the adjacent side of it. The value we know is the hypotenuse. Now remember, in reference to the angle we use, we want to choose either sin, cos, or tan. The one we choose now needs to include the adjacent side and the hypotenuse |dw:1375811355268:dw|
So which one of the 3, sin, cos, or tan has adjacent and hypotenuse?
@Psymon cos?
cos = adjacent/hypotenuse so i think @psymon meant that
ive never used them so idk im used to using 30-60-90
that's correct, because your triangle has 60, and we can predict the other angle is 90. And, 90+60+30=180
in the 30-60-90 rule the hypotenuse is TWICE as long as the SHORTEST side the "other side" is the SHORTEST side times \(\bf \sqrt{3}\)
ok so how do i do this problem
is really pretty much handed out in a silver plate, with cake and ice cream really
In a 30-60-90 triangle, the three sides of the right triangle are in the ratio of: \( 1 : \sqrt{3} : 2 \) That means that the shorter leg is 1/2 the length of the hypotenuse. The long leg is \(\sqrt{3} \) times the length of the short leg.
if "the hypotenuse is TWICE as long as the SHORTEST side" what do you think is the length of the shortest side?
Here the hypotenuse is 10. The short leg is x. From the statement "the short leg is half the length of the hyopotenuse", what can you conclude about x?
short leg is 5 :DD
so there, shortest leg is 5 and the "other leg" is THAT MUCH \(\bf \Large \times \sqrt{3}\)
Great. That is correct, the short leg, x = 5. The long leg, y, is \(\sqrt{3} \) times longer than the short leg. \( y = \sqrt{3} \times 5 \) What is y
so \[5\sqrt{3}\]
was that all i need to do???
correct \(x = 5\) \(y = 5\sqrt{3} \) That is it
wish i could give everyone a medal

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