Originally posted by smaiadon't fault me for saying so... but i'm starting to doubt your proposed solution, unless i'm missing something very important in the diagram. what similar triangles are you talking about?
Nice try, but sorry, this is not the correct answer. You don't need to develop such amazingly complicated calculations to solve this problem.
I assure you: all you need is
1- the sum of the internal angles of a triangle is 180
2- The properties of similar triangles
3- the opposite angles of two intersecting lines are equal and other axioms of euclidian geometry
Good luck.
there are many varied angles, and no triangles other than the two 30-60-90 congruent triangles (created via the initial bisector BD) that share the same angle measures.... there is a 50 degree angle, a few 60s, a 70, a 20, a 110, and angles that i could "ballpark" but in my (not very concise or intense work on this) couldn't verify algebraically. especially not for any simple round number.
and the above posted law of sines solution looks valid as far as i can tell...
Originally posted by AetheraelI'm having similar thoughts. Unless there's still some misunderstanding about the problem.
don't fault me for saying so... but i'm starting to doubt your proposed solution, unless i'm missing something very important in the diagram. what similar triangles are you talking about?
This is what I think it should look like:
http://aycu01.webshots.com/image/45880/2000590380518787909_rs.jpg
Any comments?
Originally posted by mtthwgreat picture, thats how mine looks on paper, i took your picture and added the angles i think should be in there,
I'm having similar thoughts. Unless there's still some misunderstanding about the problem.
This is what I think it should look like:
http://aycu01.webshots.com/image/45880/2000590380518787909_rs.jpg
Any comments?
http://www.sendspace.com/file/g1cd8m
Originally posted by greentGiven that it's drawn pretty much to scale, you don't find it strange that your 20 degree angle at ECD is bigger than your 40 degree angle at ECA?
great picture, thats how mine looks on paper, i took your picture and added the angles i think should be in there,
http://www.sendspace.com/file/g1cd8m
(Oh, and that file as a GIF is about 200 times smaller! π)
Originally posted by mtthwyeah, I'm probably wrong, sure wish he would post the answer now, and thanks for the tip, I'm not very good with computers yet, or Chess for that matter
Given that it's drawn pretty much to scale, you don't find it strange that your 20 degree angle at ECD is bigger than your 40 degree angle at ECA?
(Oh, and that file as a GIF is about 200 times smaller! π)
Originally posted by mtthwThe question is: what is the angle?
Again, irrelevant. It's about similifying your expressions.
I got (first attempt - will check it later):
DEC = arctan[sin(50)sin(70)/(sin(50)cos(70) + sin(60))]
No calculators in sight. Clearly not the 'simple' method you're looking for, though.
Assume you have a multiple choice test:
A- 10
B- 20
C- 30
D- 40
E- 50
Without using a calculator what is the correct answer?
Originally posted by smaiaIt's always 30º, independent of the angle you make from D to AB...
Let ABC be a triangle where AB = BC = AC.
From A, draw a line that intersects BC at a point D.
From the AD segment, draw a 20 degrees line that intersects AB at a point E. Determine the angle DEC.
This is not an easy problem.
Hint: Try to see invisible things.
Good luck. And consider yourself a genius if you resolve it in less than 30 minutes. Don't feel bad about yourself if you don't resolve it at all.
the resolution (the hard way, without triangle axioms):
- D is a middle point of BC
- angle EDC is 110º
- imagine a point F, middle point of AB (the line FD will be parallel to AC)
- angle DCF is 30º and angle FCA is 30º too
- line EA is 2 times bigger then line EF (because angle FDE is 10º and angle EDA is 20ºπ
- so, angle FCE is 10º (because FCA is 30º and is bisected by E in proportion 2:1)
- Therefore, DCE is 40º
- Therefore, DEC is 180-110-40=30
But there's an axiom for all of this... I made 10x more calculations then necessary just to show the hard way