We will try to maximize the value of the angle ACD:
For a fixed triangle ∠ABC, the ACD can be maximized when we take the median CD to be perpendicular to AB and the value of AC isas small as possible, so that the sine of ∠ACD and hence, the ∠ACD itself if maximized, as the value of AD is fixed at half ofAB at 0.5 Now, the least possible value of AC is 2. The triangle will be of sides (1,2,2) The value Sin(ACD)=