Question

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?*

Answer 1

I would think B...

Answer 2

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?

Answer 3

45º?

Answer 4

correct - so that implies it is also isoceles

Answer 5

which means AB=BC=58

Answer 6

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

Answer 7

agreed?

Answer 8

Agreed.

Answer 9

so what would AG=

Answer 10

62? I think

Answer 11

yes

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

62(60)sqrt3

Answer 17

if not, then this might help you: http://www.mathsisfun.com/algebra/trig-four-quadrants.html

Answer 18

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 :/

Answer 19

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

Answer 20

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

Answer 21

does that make sense?

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

can you work it out now?

Answer 26

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

Answer 27

ok

Answer 28

107.26 is 62*1.73

Answer 29

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