angle of 32.5438107 done with inner products.
I'm also sure of Jirakon's solution (which gives the same result)
here's a mathematica notebook for whomever is interested:
pA = {0, 0}; pB = {1/2, Sqrt[3]/2}; pC = {1, 0}; pD = {3/4, Sqrt[3]/4};
ex = x /. Solve[Tan[Pi/18]*x + Sqrt[3]/4 - 3*Tan[Pi/18]/4 == Tan[Pi/3]*x];
ey = Sqrt[3]*ex;
pE = Flatten[{ex, ey}];
ED = (pE - pD)/Sqrt[(pE - pD).(pE - pD)];
EC = (pE - pC)/Sqrt[(pE - pC).(pE - pC)];
N[ArcCos[EC.ED]*180/Pi, 10]
Originally posted by smaiaI found X=15 but i find it very hard to explain !
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.
A hunch
Is it possible the answer is 32.5 degrees?
I'm thinking of constructing a circle such that D, E, C all lie on that circle. Then if the angle subtended at the centre by D & C were 65 degrees DEC would be 32.5.
Personally I dont think this is the answer but maybe the poser thinks it is?????
Originally posted by alexdinocheck this graphic (made by jerikon)
I checked and I'm sure CED=15
Hint:draw BG,G is on AC,GBC=ECB......it would be easyer to draw.....anyway ........CED=15º
http://s117.photobucket.com/albums/o51/Jirakon/?action=view¤t=Triangle.png
is it the same triangle you have?
jerikon also posted proof in page 3 for the angle z (32.54)
I done with another method, independently, and reached the same result.
Either you understood the problem in a different way or you made an error somewhere...
Originally posted by mtthwEG is parelel to BC and it gives you GED,GEC
I'm pretty sure it's not, but I don't understand your explanation as to where G is, or how it gives you CED.
I ran it again and it seems that CED can also be 20,25???
I must be doing somthing wrong...I don't think itcan be solved without sin. or cos.
When do the 2 weeks expire?