maths problem

First, you should know angle DBC=45 (angles on a st. line),
angle EDB=70 (sum of interior angles of a 4-sided polygon=360),
angle DCB=45 (sum of interior angles of a triangle=180),
and, length BD=21m, (property of isosceles triangle)

Then, you have to do the followings:
1) Construct a point, say F, which is perpendicular from B to the line DE.
2) Draw a line connecting B and F.
3) Draw another line from B to E.

Find length of BF.
BF=21*sin(70)=19.734m

Find length of BE.
BE=sqrt(EF^2 + BF^2)
BE=sqrt(38^2 + 19.734^2)
BE=42.818m

Find angle BEF and angle AEB.
cos(angle BEF)=EF/BE=38/42.818
angle BEF=27.443
angle AEB=65-27.443=37.557

Find AB and AE.
sin(angle AEB)=AB/BE
AB=42.818m*sin(37.557)=26.100m
cos(angle AEB)=AE/BE
AE=42.818m*cos(37.557)=33.944m

33.944m

Let FD // AC ( F is a point between AE) and DG perpendicular to AC (G is a point between BC)

AB=?
FD = 38 * sin65
BG = 21 * cos45
AB = FD - BG
= 38 sin 65 - 21 cos 45
=? (自己試計啦, ok?)

AE=?
AE = AF + FE ( note:AF = GD since retangular while AG//FD and AF//DG)
= GD + FE (GD = 21* sin45; FE = 38 * cos65 )
= 21 sin45 + 38 cos65
= ? (自己試計啦, ok?)