Difficult Vector problem

[ur5pointos2sl]

< is the angle symbol here.

R is the resultant of three forces A,B,C that is R = A+B+C
If A = A<210, B=200 < Theta, C=200 <65, and R = 250 <125, use the component method to determine A and Theta.

ok so I broke them into their components and now I have no idea how to find A and Theta

Ax = A cos 30
Ay = A sin 30
Bx = 200 cos Theta or possibly could be 200 sin Theta
By = 200 sin Theta or 200 cos Theta
Cx=200 cos 65
Cy = 200 sin 65
Rx = 250 sin 35
Ry = 250 cos 35

A cos 30 + 200 cos Theta + 200 cos 65 = 250 sin 35

A sin 30 + 200 sin Theta + 200 sin 65 = 250 cos 35

would this be the correct approach? How in the world would you solve for A or Theta?

 

[Jebus_Chris]

$$Acos210+200cos\theta = 250cos135-200cos65$$
$$Asin210+200sin\theta = 250sin135-200sin65$$
You have two equations with two unknows, so you have a system and can find the variables.

 

[ur5pointos2sl]

$$Acos210+200cos\theta = 250cos135-200cos65$$
$$Asin210+200sin\theta = 250sin135-200sin65$$
You have two equations with two unknows, so you have a system and can find the variables.

I am not really sure how to solve the system. I haven't taken linear algebra and surely haven't dealt with any systems like this. Could someone please help

 

[planck42]

Just solve for A and substitute.

 

[Jebus_Chris]

Solve one for A and the plug that into the other and then you can find theta.

 

[ur5pointos2sl]

Solve one for A and the plug that into the other and then you can find theta.

ok sounds simple enough..let me try and see

 

[ur5pointos2sl]

ok sounds simple enough..let me try and see

ok maybe not so simple..I am going to have to pass on this. I cannot solve this system to save my life.

I get

A = (30.2 - 200 cos Theta)/cos 30

and

A=(23.4 - 200 sin Theta)/sin 30

not even sure if this is correct..if I plug in A then I have Cos and Sin in one equation and not sure what to do with it.

 

[planck42]

You know A in terms of $$\theta$$, so take one of your values for A and place it into the other equation. Then you'll have only constants and $$\theta$$ in the resulting equation.