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highschoolmom2010

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

  3. highschoolmom2010
    • 2 years ago
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    nope not really

  4. Psymon
    • 2 years 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
    • 2 years ago
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    that helps alot :DD

  6. Psymon
    • 2 years 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
    • 2 years ago
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    |dw:1375810320869:dw|

  8. Psymon
    • 2 years ago
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    |dw:1375810420360:dw|

  9. Psymon
    • 2 years ago
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    That kind of make sense so far?

  10. highschoolmom2010
    • 2 years ago
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    so far yes

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

  12. Psymon
    • 2 years 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
    • 2 years ago
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    im not entirely sure how to use them though

  14. Psymon
    • 2 years 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
    • 2 years ago
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    oh well yes im following ya

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

  18. highschoolmom2010
    • 2 years ago
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    @Psymon cos?

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

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

  21. Zale101
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    ok so how do i do this problem

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

  25. mathstudent55
    • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    |dw:1375817625354:dw|

  29. highschoolmom2010
    • 2 years ago
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    short leg is 5 :DD

  30. jdoe0001
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    so \[5\sqrt{3}\]

  33. highschoolmom2010
    • 2 years ago
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    @mathstudent55 @jdoe0001

  34. jdoe0001
    • 2 years ago
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    yes

  35. highschoolmom2010
    • 2 years ago
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    was that all i need to do???

  36. jdoe0001
    • 2 years ago
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    yeap

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

  38. highschoolmom2010
    • 2 years ago
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    horray thanks @mathstudent55 & @jdoe0001 & @Psmon @Zale101

  39. highschoolmom2010
    • 2 years ago
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    wish i could give everyone a medal

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