Magnitude and Acceleration Problem

[MFlood7356]

1. Three astronauts, propelled by jet backpacks, push and guide a 148 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 = 29 N, F2 = 54 N, F3 = 40 N, θ1 = 30°, and θ3 = 60°. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis) of the asteroid's acceleration?

2. F=ma

3. So I've been trying to do this problem and I can't seem to figure it out. I'm on my last attempt on my online homework so I really need some help. Here's how far I've gotten:
Ax=((29cos30)+(54cos0)+(40cos60))/148=0.667
Ay=((29sin30)+(54sin0)+(40sin60))/148=0.332
sqrt0.332²+0.667²=0.748
invertan(0.332/0.667)=26.5degrees

 

[rl.bhat]

Whether angle θ3 =60 degrees is above or below the + x-axis?

 

[MFlood7356]

The third angle is below the x axis.

 

[rl.bhat]

The third angle is below the x axis.

In that case
Ay=((29sin30)+(54sin0)+(40sin60))/148=0.332
this equation is wrong. It should be
Ay=((29sin30)+(54sin0) - (40sin60))/148=0.332

 

[MFlood7356]

So the only thing I did wrong was not negate that part?

 

[rl.bhat]

Yes.