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highschoolmom2010

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

  • 8 months ago
  • 8 months ago

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  1. highschoolmom2010
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    • 8 months ago
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  2. highschoolmom2010
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    \[h=\sqrt{2}*leg\] \[h=\sqrt{2}*\sqrt[2]{3}\]

    • 8 months ago
  3. highschoolmom2010
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    this is where im confused

    • 8 months ago
  4. mathstudent55
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    Again, a 30-60-90 triangle, so we have a \(1 : \sqrt{3} : 2 \) ratio of sides.

    • 8 months ago
  5. highschoolmom2010
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    so i have 2sqrt 3 for the side 1

    • 8 months ago
  6. mathstudent55
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    No. Be careful. The long leg is 2sqrt(3). In the ratio, the long leg is sqrt(3)

    • 8 months ago
  7. mathstudent55
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    Ratio: 1 : sqrt(3) : 2 Your triangle: y : 2sqrt(3) : x

    • 8 months ago
  8. mathstudent55
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    Since the long leg is sqrt(3) times longer than the short leg, the short leg is sqrt(3) times shorter than the long leg. Divide the long leg by sqrt(3) to get the short leg, x. Then multiply the short leg by 2 to get the hypotenuse, y.

    • 8 months ago
  9. Zale101
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    longer leg=√3*shorter leg 2√3=y√3

    • 8 months ago
  10. Zale101
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    \[\frac{ 2√3}{ √3 }*\frac{ √3}{ √3 } simplify \]

    • 8 months ago
  11. robtobey
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    \[x\text{=}2 \sqrt{3}\text{Sec}[30{}^{\circ}]\text{=}4\]\[y=2 \sqrt{3}\text{Tan}[30{}^{\circ}]=2 \]

    • 8 months ago
  12. highschoolmom2010
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    \[\frac{ 2\sqrt{3} }{ 2 }=\sqrt{3}\]

    • 8 months ago
  13. highschoolmom2010
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    @robtobey what is that

    • 8 months ago
  14. highschoolmom2010
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    @radar @hobbs978 @jdoe0001 @nincompoop @Psymon @thomaster @timo86m please can someone help me here

    • 8 months ago
  15. timo86m
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    i dont think she know trig :)

    • 8 months ago
  16. timo86m
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    its a 30 60 90 like math student said so solve the ratio :D

    • 8 months ago
  17. highschoolmom2010
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    but i get to |dw:1375832123497:dw| and no one wants to say if i am going right or not and what to do next

    • 8 months ago
  18. hobbs978
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    |dw:1375832312897:dw| does this picture help you a little

    • 8 months ago
  19. highschoolmom2010
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    yes !!!

    • 8 months ago
  20. hobbs978
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    |dw:1375832388157:dw|

    • 8 months ago
  21. highschoolmom2010
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    |dw:1375832670924:dw|

    • 8 months ago
  22. timo86m
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    math student is wrong btw those are the wrong ratios the correct are the following 30-60-90 1 : sqrt(3) : 2 y : 2sqrt(3): x we can see that 60s side is sqrt(3) times larger than 30s side so y=2sqrt(3)/sqrt(3) dividing by sqrt 3 says it is 3 times smaller than 60s side now we just evaluate y=2sqrt(3)/sqrt(3) the sqrt(3)s cancel and now you have y = 2 with me so far fill in that chart 30-60-90 1 : sqrt(3) : 2 2 : 2sqrt(3): x ^ y is now 2 :D

    • 8 months ago
  23. highschoolmom2010
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    |dw:1375833255952:dw|

    • 8 months ago
  24. highschoolmom2010
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    im soo confused

    • 8 months ago
  25. timo86m
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    30 -60 -90 1 : sqrt(3) : 2 2 : 2sqrt(3): x ^ y is now 2 from the chart we know see 90s side is twice as big as 30s side Or conversely 30s side is twice as small 2=x*2 so 90 will be 4

    • 8 months ago
  26. timo86m
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    it has to do with a 30 60 90 triangle and its ratios. They are just given in your book if not google it :) it is presumed that you know it. I dont but i googled it since i haven't in so long. in a 30 60 90 you have these ratios 30 - 60 -90 1 : sqrt(3) : 2 |dw:1375833497906:dw|

    • 8 months ago
  27. timo86m
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    |dw:1375833605135:dw|

    • 8 months ago
  28. timo86m
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    from the figure and the labeled ratios it says x is twice as big as y. Not much you can do there since they are just variables. however it does say 60s oppossite side is 2sqrt(3) and if you take the ratio of it to 30s opposite side of y it says y is sqrt(3) times smaller so you can work up an equation for that y=2*sqrt(3)/sqrt(3) here the sqrts cancel so you left with y = 2. now you can say 90s oppossite side x is twice as big as 30s opposite side y which y = 2 so therefore x is just 4 and those are your sides x=4 y=2 and of course your given angle is just your given angle :)

    • 8 months ago
  29. timo86m
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    |dw:1375834030274:dw|

    • 8 months ago
  30. timo86m
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    |dw:1375834055304:dw|

    • 8 months ago
  31. hobbs978
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    i will explain this in simple terms :) |dw:1375834066350:dw|

    • 8 months ago
  32. hobbs978
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    |dw:1375834098059:dw| plug in your a to all your sides |dw:1375834135512:dw||dw:1375834150409:dw|

    • 8 months ago
  33. hobbs978
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    but @timo86m had a very good explanation of this and would suggest go overing that this is just a summary of what he said

    • 8 months ago
  34. highschoolmom2010
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    @timo86m good explaining

    • 8 months ago
  35. highschoolmom2010
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    so x=4 and y=2

    • 8 months ago
  36. hobbs978
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    :)

    • 8 months ago
  37. highschoolmom2010
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    @hobbs978 yours was easier to understand thanks

    • 8 months ago
  38. highschoolmom2010
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    thanks to everyone that helped out :DD

    • 8 months ago
  39. robtobey
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    @timo86m Your observation regarding a lack of trig knowledge is probably true after reviewing the back and forth comments. When jumping into the middle of a problem like this, I usually post an answer that involves a minimum of narrative.

    • 8 months ago
  40. mathstudent55
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    @timo86m Why do you say my ratios are wrong and then you write exactlty the same ratios? I wrote: "Ratio: 1 : sqrt(3) : 2 Your triangle: y : 2sqrt(3) : x " You wrote: "math student is wrong btw those are the wrong ratios the correct are the following 30-60-90 1 : sqrt(3) : 2 y : 2sqrt(3): x " You have exactly the same ratios I have. How are mine wrong and yours not?

    • 8 months ago
  41. mathstudent55
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    @highschoolmom2010 In the seventh response after you posted the figure at the top, I wrote: "Divide the long leg by sqrt(3) to get the short leg, x. Then multiply the short leg by 2 to get the hypotenuse, y." Then I had to leave. I thought I was pretty much telling you exactly what to do to solve this problem, but maybe you didn't understand. To find x: "Divide the long leg by sqrt(3) to get the short leg, x." means: \( x = \dfrac { 2 \sqrt{3} } {\sqrt{3}}\) (the \(\sqrt{3} \) in the numerator and the \(\sqrt{3}\) in the denominator cancel out, so \(x = 2\) To find y: "Then multiply the short leg by 2 to get the hypotenuse, y" \(y = 2 \times 2\) \(y = 4\) BTW, above you wrote your answer as "so x=4 and y=2 ", but you switched the values of x and y.

    • 8 months ago
  42. timo86m
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    @mathstudent55 It was you that is right. BUt I copied pasted your own ratios and when i pasted them it came out all wrong. I guess it is because you used latex and the pasting didn't interpet right sorry.

    • 8 months ago
  43. timo86m
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    30-60-90 triangle, so we have a 1:3√:2 ^ SEE again when i copy paste the sqrt is not on the 3 but instead it looks like it is on the 2 And therefore i thought you had wrong ratios when in fact it was OS's or Latex's wrong doing.

    • 8 months ago
  44. mathstudent55
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    Thanks for answering. I see, but I didn't use Latex. I just copied and pasted myself to show you what I had written above. This is very strange.

    • 8 months ago
  45. highschoolmom2010
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    @mathstudent55 i am more a visual learner so @hobbs978 showing me was easier yes you answer is correct too so thanks @mathstudent55

    • 8 months ago
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