Question

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

Answer 1

The most rel and correct answer is 8.3

Answer 2

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