highschoolmom2010
  • highschoolmom2010
Find the value of each variable. If your answer is not an integer, express it in simplest radical form
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
highschoolmom2010
  • highschoolmom2010
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Psymon
  • Psymon
Do you know your trig functions? Like what sin, cos, tan are in regards to a triangle?
highschoolmom2010
  • highschoolmom2010
nope not really

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Psymon
  • Psymon
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.
highschoolmom2010
  • highschoolmom2010
that helps alot :DD
Psymon
  • Psymon
\[\sin = \frac{ opposite side }{ hypotenuse }\] \[\cos = \frac{ adjacent side }{ hypotenuse }\] \[\tan = \frac{ opposite side }{ adjacent side }\] 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.
Psymon
  • Psymon
|dw:1375810320869:dw|
Psymon
  • Psymon
|dw:1375810420360:dw|
Psymon
  • Psymon
That kind of make sense so far?
highschoolmom2010
  • highschoolmom2010
so far yes
Psymon
  • Psymon
Okay, cool. So this is your triangle that we have then: |dw:1375810542321:dw|
Psymon
  • Psymon
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?
highschoolmom2010
  • highschoolmom2010
im not entirely sure how to use them though
Psymon
  • Psymon
Right, we're getting to that :P I just wanted to see if you were following me so far.
highschoolmom2010
  • highschoolmom2010
oh well yes im following ya
Psymon
  • Psymon
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|
Psymon
  • Psymon
So which one of the 3, sin, cos, or tan has adjacent and hypotenuse?
highschoolmom2010
  • highschoolmom2010
@Psymon cos?
Zale101
  • Zale101
cos = adjacent/hypotenuse so i think @psymon meant that
highschoolmom2010
  • highschoolmom2010
ive never used them so idk im used to using 30-60-90
Zale101
  • Zale101
that's correct, because your triangle has 60, and we can predict the other angle is 90. And, 90+60+30=180
jdoe0001
  • jdoe0001
in the 30-60-90 rule the hypotenuse is TWICE as long as the SHORTEST side the "other side" is the SHORTEST side times \(\bf \sqrt{3}\)
highschoolmom2010
  • highschoolmom2010
ok so how do i do this problem
jdoe0001
  • jdoe0001
is really pretty much handed out in a silver plate, with cake and ice cream really
mathstudent55
  • mathstudent55
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.
jdoe0001
  • jdoe0001
if "the hypotenuse is TWICE as long as the SHORTEST side" what do you think is the length of the shortest side?
mathstudent55
  • mathstudent55
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?
highschoolmom2010
  • highschoolmom2010
|dw:1375817625354:dw|
highschoolmom2010
  • highschoolmom2010
short leg is 5 :DD
jdoe0001
  • jdoe0001
so there, shortest leg is 5 and the "other leg" is THAT MUCH \(\bf \Large \times \sqrt{3}\)
mathstudent55
  • mathstudent55
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
highschoolmom2010
  • highschoolmom2010
so \[5\sqrt{3}\]
highschoolmom2010
  • highschoolmom2010
@mathstudent55 @jdoe0001
jdoe0001
  • jdoe0001
yes
highschoolmom2010
  • highschoolmom2010
was that all i need to do???
jdoe0001
  • jdoe0001
yeap
mathstudent55
  • mathstudent55
correct \(x = 5\) \(y = 5\sqrt{3} \) That is it
highschoolmom2010
  • highschoolmom2010
horray thanks @mathstudent55 & @jdoe0001 & @Psmon @Zale101
highschoolmom2010
  • highschoolmom2010
wish i could give everyone a medal

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