Question 1205848
<pre>
I labeled the trapezoid clockwise instead of counter-clockwise. To make
it labeled counter-clockwise, draw the mirror image of this drawing.

{{{drawing(400,240,-1,9,-1,5,

line(0,0,4.5,0), line(0,0,2,2sqrt(3)), line(2,2sqrt(3),4.5+2sqrt(3),2sqrt(3)),
line(4.5+2sqrt(3),2sqrt(3),4.5,0),
locate(0,0,A), locate(4.5,0,D), locate(8,3.8,C), locate(2,3.9,B),
locate(.4,.7,60^o), locate(6.9,3.5,45^o),

green(line(2,0,2,2sqrt(3)),line(4.5,0,4.5, 2sqrt(3))), locate(2,0,E),
locate(4.5,3.9,F)




)}}}

Braw BE and FD perpendicular to AD and BC.

{{{AE/AB=cos("<A")}}}
{{{AE=AB*cos("<A")=4*cos(60^o)=4(1/2)=2}}}

{{{EB/AB=sin("<A")}}}
{{{EB=AB*sin("<A")=4*sin(60^o)=4(sqrt(3)/2)=2sqrt(3)}}}

{{{ED=AD-AE=4-2=2}}}

{{{BF=ED=2}}}

{{{DF=EB=2sqrt(3)}}}

Since angle C is 45<sup>o</sup>, that tells us that triangle DFC is an
isosceles right triangle. The hyptenuse of an isosceles right triangle is
{{{sqrt(2)}}} times either leg.


{{{DC = DF*sqrt(3) = 2sqrt(3)*sqrt(2)=2sqrt(6) }}}

Edwin</pre>