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
