What is the length of the line ab a. 8 b. 8.3 c. 6.6 6. 9.7

We know that
in the right triangle ACD
Applying the Pythagoras theorem
AC²=AD²+CD²> AD²=AC²-CD²> AD²=5²-4²---> AD²=9> AD=3

let
∅=angle CAD
tan ∅=4/3 

in the right triangle CDB
the angle DCB is equal to ∅
tan ∅=DB/CD> DB=CD*tan ∅> DB=4*(4/3)> DB=16/3

AB=AD+DB> 3+16/3> AB=25/3> AB=8.33

the answer is
b. 8.3