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Newton's Law Question Involving Tow Truck

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Homework Statement


A tow truck pulls on a stuck car with a force of 3000N. The tow cable is under tension and pulls downward and to the left on the pin at its upper end. The pin is held in equilibrium by forces exerted by 2 bars A and B which are connected to the pin.

The diagram shows that the tow cable is at 60 degrees to the vertical, strut A is vertical and strut B is at 50 degrees to the horizontal. ( I hope this is clear)

Determine the force on each strut and whether it is of tension or compression.


Homework Equations


Newton's Laws


The Attempt at a Solution



I didn't take the forces (normal, friction and weight) of the car into account because I didn't think they were relevant to this question and I don't think I have enough given numerical values anyway...
Having drawn a free body diagram, I determined that the force on A was of tension and force on B was of compression.
Tc = tension of cable = 3000N
Ta = tension of strut A
Tb =compression force of strut B

Hence:
sigma(Fx)=Tcsin60 +Tbcos50 = 0
which gives Tb = 947.631...N = 950N
sigma(Fy)=Tccos60 +Ta +Tbsin50=0
substituting Tb gives Ta = 2608.604...N =2700N

But the answers are wrong. I think that at least the sum of my forces in the x direction are incorrect...but I don't know what to do because all i have is the applied force and angles...
 
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