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rebeccaskell94 Group Title

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?*

  • 2 years ago
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  1. Pac1f1cIslander Group Title
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    I would think B...

    • 2 years ago
  2. asnaseer Group Title
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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?

    • 2 years ago
  3. rebeccaskell94 Group Title
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    45º?

    • 2 years ago
  4. asnaseer Group Title
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    correct - so that implies it is also isoceles

    • 2 years ago
  5. asnaseer Group Title
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    which means AB=BC=58

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

    • 2 years ago
  7. asnaseer Group Title
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    agreed?

    • 2 years ago
  8. rebeccaskell94 Group Title
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    Agreed.

    • 2 years ago
  9. asnaseer Group Title
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    so what would AG=

    • 2 years ago
  10. rebeccaskell94 Group Title
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    62? I think

    • 2 years ago
  11. asnaseer Group Title
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    yes

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

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

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

    • 2 years ago
  15. asnaseer Group Title
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    are you familiar with trigonometry (sin/cos/tan)?

    • 2 years ago
  16. Pac1f1cIslander Group Title
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    62(60)sqrt3

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

    • 2 years ago
  18. rebeccaskell94 Group Title
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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 :/

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

    • 2 years ago
  20. asnaseer Group Title
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    which implies:\[GE=62\times\tan(60)\]

    • 2 years ago
  21. asnaseer Group Title
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    does that make sense?

    • 2 years ago
  22. rebeccaskell94 Group Title
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    Ah! Yes. I think so. I had to figure out where the 62 came from again xD

    • 2 years ago
  23. asnaseer Group Title
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    good, now some angles have /well known/ values for sin/cos/tan

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

    • 2 years ago
  25. asnaseer Group Title
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    can you work it out now?

    • 2 years ago
  26. rebeccaskell94 Group Title
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    Let me try, and then I'll post it :D

    • 2 years ago
  27. asnaseer Group Title
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    ok

    • 2 years ago
  28. rebeccaskell94 Group Title
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    107.26 is 62*1.73

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

    • 2 years ago
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