The answers I recieved are a bit confusing (Meaning that either the person didn't explain very well or that I haven't learned about the stuff yet)
The answer is correct!!!
In order to solve this problem, you need to know basic trigonometry. I don't see any other method to solve this 'cookie'.
BD = CD = 4 BI = 5 DI = 4
In order to find the length of AD, you have to find angle B and multiply its tangent by 4.
[ABC] = BD * AD