Let me see.
sin A =opposite/hypotenuse
cos A = adjacent/hypotenuse
Look at the diagram.
Clearly, opposite angle A we have 3.
The hypotenuse is 5.
So, we conclude that sin A = 3/5.
Go back to the diagram.
The height of the triangle is the adjacent side to angle A for this problem.
Think about it this way:
The adjacent side is the height 4.
The hypotenuse we know as 5.
So, cos A = 4/5.
The answer is choice A