The hardest easy geometry problem in the world... please help!

[Bioture]

We went to an old family friend's restaurant in Maryland

Here's a hint, lengths of sides on a triangle are proportional to the angle opposite them

I realize that, but we're not supposed to use proportions or anything algebraic. It's what geekbot says. Basic geometry only. So anything where you're solving for x is out.

[The Hawk]

i figured it out in like 5 minutes useing basic geometry, too lazy to write the proof though.

[D1st0rt]

GOGDMANIT i used law of sines to make one of em isosceles without realizing

back to drawing board

well, what i gather from this is that any easy problem can be made irrationally complicated

[deathking]

Here's a hint, lengths of sides on a triangle are proportional to the angle opposite them

eh...no?
ur thinking of sin(A)/a = k?

i solved it. (answer and mini hint below.

x = 20

2 crucial parts for me.

-extend a line from d to the other side, parallel to AB
-realize that triangle CDE is similar to triangle EDB

I dont think its possible to solve it in 2 or 5 min =/

[Zeebu]

couple hints to the way i think it should be done

draw a parallel line to AB, start it from D and go straight over. I called that point F

now draw a line from A to F

note the intersection of the line you just drew AF to DB... i called it G

now, that makes angle BAF = 60
that also makes BAF=AFD=ABD=FBD=60
also CBA=CFD=80

now draw a circle that contains triangle BEA
now make the center of your circle H
we all know how a cirlce works... so now you have HB=HE=HA

i will post some more later... i just plain ol dont feel like starting up paint yet... but itd be better to stop and see what we have so far up to this point

finagle the numbers a bit and you'll see that H and G are on the same point

from then on its pretty easy

my couple hints went on to explaining half the problem for you. or at least setting it up

[Twerp]

Sent you the finished visual. Sorry, went o ut to the movies.

[Bioture]

looking at twerp's proof. it's legit. I didn't figure out the "similar triangles" one

[PolluX]

you guys that claim to get it so fast, how are you doing it?

it took me a while... i had to break out my compass =/

i dont think you can do it using only algebra

edit: if i can make it in paint (ugh) ill oput my solution up later

yes, guys this isn't easy. I took me one day. it's like zeebu said, you really need to sit down and draw some shit.

2 minutes.... pfff cundor one time when a thread isn't about sex, you still share your performances with us!

[Arikel]

It really just takes you 5 minutes... what you need to do is follow a simple guideline and try to figure out all the triangles that are possible in that picture, after that start calculating the angles, you will see that it's really easy to solve it the more triangles you can figure out the easier it will be to get the result.

[Bioture]

ok that's long enough. here is twerp's proof:

http://img72.imageshack.us/img72/895...inishedbt3.png

did anyone solve it another way.

[GuruMeditation]

http://img72.imageshack.us/img72/895...inishedbt3.png

Imageshack is the answer? How spiritual.

[Cops]

Sometimes I wish I did better than a 56 in Grade 11 math.