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highschoolmom2010

  • one year ago

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

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  1. highschoolmom2010
    • one year ago
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  2. Psymon
    • one year ago
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    Do you know your trig functions? Like what sin, cos, tan are in regards to a triangle?

  3. highschoolmom2010
    • one year ago
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    nope not really

  4. Psymon
    • one year ago
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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.

  5. highschoolmom2010
    • one year ago
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    that helps alot :DD

  6. Psymon
    • one year ago
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    \[\sin = \frac{ opposite side }{ hypotenuse }\] \[\cos = \frac{ adjacent side }{ hypotenuse }\] \[\tan = \frac{ opposite side }{ adjacent side }\] 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.

  7. Psymon
    • one year ago
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    |dw:1375810320869:dw|

  8. Psymon
    • one year ago
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    |dw:1375810420360:dw|

  9. Psymon
    • one year ago
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    That kind of make sense so far?

  10. highschoolmom2010
    • one year ago
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    so far yes

  11. Psymon
    • one year ago
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    Okay, cool. So this is your triangle that we have then: |dw:1375810542321:dw|

  12. Psymon
    • one year ago
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    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?

  13. highschoolmom2010
    • one year ago
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    im not entirely sure how to use them though

  14. Psymon
    • one year ago
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    Right, we're getting to that :P I just wanted to see if you were following me so far.

  15. highschoolmom2010
    • one year ago
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    oh well yes im following ya

  16. Psymon
    • one year ago
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    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|

  17. Psymon
    • one year ago
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    So which one of the 3, sin, cos, or tan has adjacent and hypotenuse?

  18. highschoolmom2010
    • one year ago
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    @Psymon cos?

  19. Zale101
    • one year ago
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    cos = adjacent/hypotenuse so i think @psymon meant that

  20. highschoolmom2010
    • one year ago
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    ive never used them so idk im used to using 30-60-90

  21. Zale101
    • one year ago
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    that's correct, because your triangle has 60, and we can predict the other angle is 90. And, 90+60+30=180

  22. jdoe0001
    • one year ago
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    in the 30-60-90 rule the hypotenuse is TWICE as long as the SHORTEST side the "other side" is the SHORTEST side times \(\bf \sqrt{3}\)

  23. highschoolmom2010
    • one year ago
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    ok so how do i do this problem

  24. jdoe0001
    • one year ago
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    is really pretty much handed out in a silver plate, with cake and ice cream really

  25. mathstudent55
    • one year ago
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    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.

  26. jdoe0001
    • one year ago
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    if "the hypotenuse is TWICE as long as the SHORTEST side" what do you think is the length of the shortest side?

  27. mathstudent55
    • one year ago
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    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?

  28. highschoolmom2010
    • one year ago
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    |dw:1375817625354:dw|

  29. highschoolmom2010
    • one year ago
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    short leg is 5 :DD

  30. jdoe0001
    • one year ago
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    so there, shortest leg is 5 and the "other leg" is THAT MUCH \(\bf \Large \times \sqrt{3}\)

  31. mathstudent55
    • one year ago
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    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

  32. highschoolmom2010
    • one year ago
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    so \[5\sqrt{3}\]

  33. highschoolmom2010
    • one year ago
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    @mathstudent55 @jdoe0001

  34. jdoe0001
    • one year ago
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    yes

  35. highschoolmom2010
    • one year ago
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    was that all i need to do???

  36. jdoe0001
    • one year ago
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    yeap

  37. mathstudent55
    • one year ago
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    correct \(x = 5\) \(y = 5\sqrt{3} \) That is it

  38. highschoolmom2010
    • one year ago
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    horray thanks @mathstudent55 & @jdoe0001 & @Psmon @Zale101

  39. highschoolmom2010
    • one year ago
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    wish i could give everyone a medal

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