What Causes the Difference in Calculated Angles in Inelastic Collision Problems?

[teknodude]

After a completely inelastic collision, two objects of the same mass and initial speed are found to move away together at 1/2 their initial speed. Find the angle between the initial velocities of the objects.

Solution is here http://www.physics.sfsu.edu/~senglish/APphysicswebsite/collisions/solutions%20on%20collisions/17.pdf

My first atempt to solve this problem was drawing my diagram so that both objects converge towards the positive y-axis instead of the positive x-axis as seen in solution.

v=initial velocity vf= final velocity
so the x-comp mv cos A - mv cos B= 0
y-comp mv sin A + mv sin A = 2m vf

Well it didn't work, so i gave up and redrew my diagram like the one in the solution and solved it that way. I'm starting to conclude that my original idea solved for a different angle for the problem.

What did i do wrong in solving the problem with my original diagram with the objects converging towards the positive y-axis

 

[Hyperreality]

NOTE:
The x component momentum is

mv cosA - mv cosB = 0

not

mv cosA - mv sinA

 

[teknodude]

NOTE:
The x component momentum is

mv cosA - mv cosB = 0

not

mv cosA - mv sinA

typo

anyway your right

my calculations so far
x-comp mv cos A - mv cos B= 0 A=b but then its 0=0 which doesn;t really help

so looking at the y-comp
y-comp mv sin A + mv sin A = 2m vf

2mv sinA = 2mv 1/2v

sin A = 1/2
A= 30 degrees x2 60 degrees

The answer is suppose to be 120 degrees, but then my answer plus the actual is 180 degrees. Therefore i think the angle i solved for was the outside angle, but why