# Difficult Vector problem

• ur5pointos2sl

#### 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?

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

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$$Acos210+200cos\theta = 250cos135-200cos65$$
$$Asin210+200sin\theta = 250sin135-200sin65$$
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

Just solve for A and substitute.

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

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

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. 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.