On February 07 2009 23:12 Cpt Obvious wrote:
Ok thanks, I think I understood that. That's trigonometry though, not algebra. Algebra is what I tried to do

Still can't grasp why it's impossible to solve with my path, but hey, that's math.

No it's lack of understanding of maths

b3tty

Canada216 Posts

February 07 2009 21:29 GMT

#42

+ Show Spoiler [Easier Solution] +

found an easier way to solve it then the way i suggested before

i think this works.. if not, point out my errors, cheers!

extend BC out
connect the top line of the smaller triangle to this extended line
you have now created a new isosceles triangle
you know the large angle of this triangle is 120 degrees
you can solve for the two smaller angles because they are equal.

X = 80

+ Show Spoiler [Diagram] +

ydg

United States690 Posts

February 07 2009 21:51 GMT

#43

How do you know that the new triangle is isoceles?

minus_human

4784 Posts

February 07 2009 22:24 GMT

#44

Since your triangle looks isosceles, it probably isn't. As I've mentioned before, that drawing, the one u based your solution upon, is incorrect. The angles aren't really what it is written on them. So if your triangle looks isosceles on the wrong drawing, it most probably has way disproportionate angles on an accurate drawing, therefore it isn't isosceles

..unless you have an explanation to why beta = alfa, I haven't bothered to verify what I wrote above

Cpt Obvious

Germany3073 Posts

February 07 2009 23:32 GMT

#45

I also don't get how you know that the other angle is 100 degrees. Can you elaborate on that?

This solution looks elegant if it is correct, but I am not sure of that.

b3tty

Canada216 Posts

February 08 2009 00:02 GMT

#46

the other angle is 100 because 60 + 20 = 80

100 degrees is missing from the straight line

and you guys are right, i have no way of proving that the new triangle is isoceles, this solution is wrong.

gonna draw up my original one later on today
and see if i messed up there again.

Malongo

Chile3472 Posts

February 08 2009 01:01 GMT

#47

Wow im actually glad this thread interested some people 1200 or so visits is good for a mathematics related one thank you guys, im still stucked in sigma_x's continuation, so im not writing my solution yet (but i guess its still fun for those still interested). I just want to add that the "pure algebra" doesnt work (cpt obbious and others first attempt) because it relies only in the a+b+c=180 formula and keeps away other data (namely linear data ac=ab and others).

b3tty

Canada216 Posts

February 08 2009 01:20 GMT

#48

i used a protractor and determined that the angle is 80 degrees.
however, i have no solid way of proving it without using trigonometric calculations (sin, cos, tan)

is it possible to solve it using only angles?

koreakool

United States334 Posts

February 08 2009 02:26 GMT

#49

On February 08 2009 10:20 b3tty wrote:
i used a protractor and determined that the angle is 80 degrees.
however, i have no solid way of proving it without using trigonometric calculations (sin, cos, tan)

is it possible to solve it using only angles?

I dunno I tried but my linear algebra sucks
I have 4 equations that I can't solve simultaneously
Although I do know I'm on the right track because I keep proving that my equations are correct -_-;;

Malongo

Chile3472 Posts

February 08 2009 02:47 GMT

#50

Yes. Ill post the solution later as i said (in fact my point here is finding another solutions check the spoiler in the op if you want dome hint full solution is not up yet)

On February 08 2009 11:26 koreakool wrote:
I dunno I tried but my linear algebra sucks
I have 4 equations that I can't solve simultaneously
Although I do know I'm on the right track because I keep proving that my equations are correct -_-;;

You need more geometry than algebra for this, algebra skips some data.

ydg

United States690 Posts

February 08 2009 03:01 GMT

#51

On February 08 2009 11:47 malongo wrote:

Show nested quote +

Yes. Ill post the solution later as i said (in fact my point here is finding another solutions check the spoiler in the op if you want dome hint full solution is not up yet)

Show nested quote +

You need more geometry than algebra for this, algebra skips some data.

My solution uses pure algebra and trigonometric rules

Malongo

Chile3472 Posts

February 08 2009 04:43 GMT

#52

On February 08 2009 12:01 ydg wrote:

Show nested quote +

My solution uses pure algebra and trigonometric rules

Omg i didnt saw that.... hey cheater X=79.crap!!! ahah i guess its more messy by pure geometry, but thats what i wanted an alternative solution thanX a lot im so bad at trigonometry.

Cpt Obvious

Germany3073 Posts

February 08 2009 13:48 GMT

#53

Well the 79.9986342 degrees is just from rounding odd numbers during the calculation, and since you only have whole degrees in every other angle of the triangles, it's pretty safe to assume that x is a whole number too.

@b3tty: I think I've proven that the algebraic attempt using only angles doesn't give a determinate solution. This is because I am missing one bit of information to include into my system of equations, and it ends up being indeterminate. All it does is prove that 180=180, basically.
I will not conclude that it is impossible, but I don't see where that additional information should come from but trigonometry. I did use AB=AC by calculating the angles complementing the 50 and 60 degree angles in the corners, so that can't be it.