In quadrilateral BCED, we have BD = 11, BC = 9, and CE=2. Sides BD andCE are extended past B and C, respectively, to meet at point A. If AC = 20 and AB = 24, then what is DE?
Something like this
C
2 E
9 18
B 9 D 15 A
Law of Cosines
9^2 = 24^2 + 20^2 -2 (20) (24)cos (CAB)
[9^2 - 24^2 - 20^2] / [ -2 (20) (24) ] = cos (CAB)
179/192 = cos (CAB) = cos(EAD)
And again
ED^2 = 15^2 + 18^2 - 2 (15)(18) cos (EAD)
ED^2 = 15^2 + 18^2 - 2 ( 15)(18)(179/192)
ED^2 = 729 / 16
ED = sqrt (729)/ 4
ED = sqrt (3^6) / 4
ED = (3^6)^(1/2) / 4
ED = 3^3 / 4
ED = 27/4 = 6.75