## anonymous 4 years ago 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?*

1. anonymous

I would think B...

2. 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?

3. anonymous

45º?

4. asnaseer

correct - so that implies it is also isoceles

5. asnaseer

which means AB=BC=58

6. anonymous

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

7. asnaseer

agreed?

8. anonymous

Agreed.

9. asnaseer

so what would AG=

10. anonymous

62? I think

11. asnaseer

yes

12. asnaseer

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

13. asnaseer

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

14. anonymous

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

15. asnaseer

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

16. anonymous

62(60)sqrt3

17. asnaseer

18. 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 :/

19. asnaseer

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

20. asnaseer

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

21. asnaseer

does that make sense?

22. anonymous

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

23. asnaseer

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

24. asnaseer

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

25. asnaseer

can you work it out now?

26. anonymous

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

27. asnaseer

ok

28. anonymous

107.26 is 62*1.73

29. asnaseer

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