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rebeccaskell94

n the figure below, the length of line segment CB is 58 units and the length of line segment BG is 120 units. What is the length of line segment GE? http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0404_07/image0084e2ee688.gif 62√3 116 58√2 124 *I think the answer is C?*

  • one year ago
  • one year ago

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  1. Pac1f1cIslander
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    I would think B...

    • one year ago
  2. asnaseer
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    look at the first triangle ABC - notice it is a right-angled triangle and one of the angles is 45, so what would the other angle be?

    • one year ago
  3. rebeccaskell94
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    45º?

    • one year ago
  4. asnaseer
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    correct - so that implies it is also isoceles

    • one year ago
  5. asnaseer
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    which means AB=BC=58

    • one year ago
  6. Pac1f1cIslander
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    Oh, they're both special triangles...one is 45-45-90, the other is 30-60-90

    • one year ago
  7. asnaseer
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    agreed?

    • one year ago
  8. rebeccaskell94
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    Agreed.

    • one year ago
  9. asnaseer
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    so what would AG=

    • one year ago
  10. rebeccaskell94
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    62? I think

    • one year ago
  11. asnaseer
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    yes

    • one year ago
  12. asnaseer
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    now use the fact that:\[\cos(60)=0.5\]to work out AE

    • one year ago
  13. asnaseer
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    sorry - use the fact that:\[\tan(60)=\sqrt(3)\]to work out GE

    • one year ago
  14. rebeccaskell94
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    Well, I'm not really sure how to do that. Sorry, I'm dumb when it comes to math. :/

    • one year ago
  15. asnaseer
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    are you familiar with trigonometry (sin/cos/tan)?

    • one year ago
  16. Pac1f1cIslander
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    62(60)sqrt3

    • one year ago
  17. asnaseer
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    if not, then this might help you: http://www.mathsisfun.com/algebra/trig-four-quadrants.html

    • one year ago
  18. rebeccaskell94
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    Vaguely, yes. I took geometry 3 years ago and got a B+ and A- but I don't remember most of it :/ I'm trying desperately to help a friend but some of this stuff I just don't remember. I know that tan = opposite ÷ adjacent cos= adjacent ÷ hypotenuse sin= opposite ÷ hypotenuse If I remember those correctly. I'm personally, currently in AlgII :/

    • one year ago
  19. asnaseer
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    good, so look at triangle AEG and note that:\[\tan(60)=\frac{GE}{AG}=\frac{GE}{62}\]

    • one year ago
  20. asnaseer
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    which implies:\[GE=62\times\tan(60)\]

    • one year ago
  21. asnaseer
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    does that make sense?

    • one year ago
  22. rebeccaskell94
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    Ah! Yes. I think so. I had to figure out where the 62 came from again xD

    • one year ago
  23. asnaseer
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    good, now some angles have /well known/ values for sin/cos/tan

    • one year ago
  24. asnaseer
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    60 is one such angle where: \(\tan(60)=\sqrt{3}\)

    • one year ago
  25. asnaseer
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    can you work it out now?

    • one year ago
  26. rebeccaskell94
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    Let me try, and then I'll post it :D

    • one year ago
  27. asnaseer
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    ok

    • one year ago
  28. rebeccaskell94
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    107.26 is 62*1.73

    • one year ago
  29. asnaseer
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    roughly yes - you should leave it in terms of the radical, so the answer is \(62\sqrt{3}\)

    • one year ago
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