anonymous
  • anonymous
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?*
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I would think B...
asnaseer
  • asnaseer
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?
anonymous
  • anonymous
45º?

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asnaseer
  • asnaseer
correct - so that implies it is also isoceles
asnaseer
  • asnaseer
which means AB=BC=58
anonymous
  • anonymous
Oh, they're both special triangles...one is 45-45-90, the other is 30-60-90
asnaseer
  • asnaseer
agreed?
anonymous
  • anonymous
Agreed.
asnaseer
  • asnaseer
so what would AG=
anonymous
  • anonymous
62? I think
asnaseer
  • asnaseer
yes
asnaseer
  • asnaseer
now use the fact that:\[\cos(60)=0.5\]to work out AE
asnaseer
  • asnaseer
sorry - use the fact that:\[\tan(60)=\sqrt(3)\]to work out GE
anonymous
  • anonymous
Well, I'm not really sure how to do that. Sorry, I'm dumb when it comes to math. :/
asnaseer
  • asnaseer
are you familiar with trigonometry (sin/cos/tan)?
anonymous
  • anonymous
62(60)sqrt3
asnaseer
  • asnaseer
if not, then this might help you: http://www.mathsisfun.com/algebra/trig-four-quadrants.html
anonymous
  • anonymous
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 :/
asnaseer
  • asnaseer
good, so look at triangle AEG and note that:\[\tan(60)=\frac{GE}{AG}=\frac{GE}{62}\]
asnaseer
  • asnaseer
which implies:\[GE=62\times\tan(60)\]
asnaseer
  • asnaseer
does that make sense?
anonymous
  • anonymous
Ah! Yes. I think so. I had to figure out where the 62 came from again xD
asnaseer
  • asnaseer
good, now some angles have /well known/ values for sin/cos/tan
asnaseer
  • asnaseer
60 is one such angle where: \(\tan(60)=\sqrt{3}\)
asnaseer
  • asnaseer
can you work it out now?
anonymous
  • anonymous
Let me try, and then I'll post it :D
asnaseer
  • asnaseer
ok
anonymous
  • anonymous
107.26 is 62*1.73
asnaseer
  • asnaseer
roughly yes - you should leave it in terms of the radical, so the answer is \(62\sqrt{3}\)

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