## 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 2 years ago

1. Pac1f1cIslander Group Title

I would think B...

2. asnaseer Group Title

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?

45º?

4. asnaseer Group Title

correct - so that implies it is also isoceles

5. asnaseer Group Title

which means AB=BC=58

6. Pac1f1cIslander Group Title

Oh, they're both special triangles...one is 45-45-90, the other is 30-60-90

7. asnaseer Group Title

agreed?

Agreed.

9. asnaseer Group Title

so what would AG=

62? I think

11. asnaseer Group Title

yes

12. asnaseer Group Title

now use the fact that:$\cos(60)=0.5$to work out AE

13. asnaseer Group Title

sorry - use the fact that:$\tan(60)=\sqrt(3)$to work out GE

Well, I'm not really sure how to do that. Sorry, I'm dumb when it comes to math. :/

15. asnaseer Group Title

are you familiar with trigonometry (sin/cos/tan)?

16. Pac1f1cIslander Group Title

62(60)sqrt3

17. asnaseer Group Title

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 :/

19. asnaseer Group Title

good, so look at triangle AEG and note that:$\tan(60)=\frac{GE}{AG}=\frac{GE}{62}$

20. asnaseer Group Title

which implies:$GE=62\times\tan(60)$

21. asnaseer Group Title

does that make sense?

Ah! Yes. I think so. I had to figure out where the 62 came from again xD

23. asnaseer Group Title

good, now some angles have /well known/ values for sin/cos/tan

24. asnaseer Group Title

60 is one such angle where: $$\tan(60)=\sqrt{3}$$

25. asnaseer Group Title

can you work it out now?

Let me try, and then I'll post it :D

27. asnaseer Group Title

ok

roughly yes - you should leave it in terms of the radical, so the answer is $$62\sqrt{3}$$