We have something like this :
A
3
D E
4
B C
Since DE is parallel to BC, by Euclid........AD/DB = AE/ EC
And AE = 9 - EC .....so we have.....
3 / 4 = [9 - EC] / EC cross-multiply
3EC = 4 [9 - EC]
3EC = 36 - 4EC
7EC = 36 divide both sides by 7
EC = 36/7 = about 5.14 ft ....So E should be about 5.14 ft from C on AC
Proof :
Note = AE = 9 - EC = 9 - 36/7 = 27/7
So
AD/DB = AE/EC
3/4 = [27/7] / [36/7]
3/4 = 27/26
3/4 = 3/4
