Harder than you think!

A nice triangle geometry question harder than it seems.
Solution of the problem requires the use of;
Congruent triangles,
Properties of isosceles triangles
Special triangles.
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[@Grizzly01-vr4pn]

Same as video up to 0:30
in △AED: AD = √3/sin40°
Law of sines in △ABD: AD/sin60° = x/sin40°
Substitute for AD and rearrange, so x = (√3)sin40°/(sin40°)(sin60°) = √3/sin60° = √3/(√3/2) = (2√3)/√3 = 2

[@zdrastvutye]

either do 2 equations with 2 unknown numbers or calculate the 3rd angle in triangle bcd and apply the sinus formula:
10 print "geosolve-harder than you think":dim x(1,2),y(1,2):w1=40:w2=10
20 l1=2*sqr(3):h1=l1/2*tan(rad(w1+w2)):l3=sqr(h1^2+l1^2/4)
30 dx=l1*sin(rad(w2))/sin(rad(180-2*w2-w1)):lx=l3-dx
40 print "x=";lx:x(0,0)=0:y(0,0)=0:x(0,1)=l1:y(0,1)=0:x(0,2)=(l3-lx)*cos(rad(w1+w2))
50 x(0,2)=x(0,1)-x(0,2):y(0,2)=(l3-lx)*sin(rad(w1+w2)):x(1,0)=0:y(1,0)=0:x(1,1)=x(0,2)
55 y(1,1)=y(0,2):x(1,2)=l1/2:y(1,2)=h1:masx=1200/l1:masy=900/h1
70 if masx
run in bbc basic sdl and hit ctrl tab to copy from the results window.
as a schoolboy, i did calculations like that with my pocket calculator as follows:
read the result, write it on paper, input it in next equation, write next result on paper...

[@GeoSolve]

Thanks for sharing your solution.