ED = 17 = EF and
angle DEG = angle FEG. Therefore,
Triangles DEG and FEG are congruent.
Thus, DG = FG. Therefore,
20^2 + AG^2 = DA^2 + AG^2
= DG^2 = FG^2
= GB^2 + BF^2
= GB^2 + 5^2
or
GB^2  AG^2 = 20^2  5^2
or
(GB  AG)(GB + AG)
= (GB  AG)(25) = (20  5)(25)
Thus,
GB  AG = 15
GB + AG = 25
Therefore, AG = 5. Thus,
EG = sqrt(DA^2 + [DE  AG]^2)
= sqrt(20^2 + 12^2)
= sqrt(544) ~= 23.3238

Posted by Bractals
on 20101107 14:15:50 