(a) Let A B C D be an isosceles trapezoid with A B=C D=5, B C=2, A D=8. Find the height of the trapezoid and the length of its diagonals.
(b) For the trapezoid introduced in (a), find the exact value of \cos \angle A B C.
(c) In triangle K L M, let points G and E be on segment L M so that \angle M K G=\angle G K E= \angle E K L=\alpha. Let point F be on segment K L so that G F is parallel to K M. Given that K F E G is an isosceles trapezoid and that \angle K L M=84^{\circ}, determine \alpha.
