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Math Help - confusing vector problem

  1. #1
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    confusing vector problem

    < is angle symbol

    R is the resultant of the 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(there may be 2 solutions)

    So

    Ax= A cos 30
    Ay= A sin 30
    Bx=200 cos Theta(possibly could be switched)
    By=200 sin Theta
    Cx=200 cos 65 = 84.5
    Cy=200 sin 65 = 181
    Rx=250 sin 35 = 114.7
    Ry=250 cos 35 = 204.7

    A cos 30 + 200 cos Theta = 30.2

    is this the correct way to do this problem? Where would I go from here since I have 2 variables? any help to give me a shove would be appreciated.
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  2. #2
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    Quote Originally Posted by ur5pointos2slo View Post
    < is angle symbol

    R is the resultant of the 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(there may be 2 solutions)

    So

    Ax= A cos 30
    Ay= A sin 30
    Bx=200 cos Theta(possibly could be switched)
    By=200 sin Theta
    Cx=200 cos 65 = 84.5
    Cy=200 sin 65 = 181
    Rx=250 sin 35 = 114.7
    Ry=250 cos 35 = 204.7

    A cos 30 + 200 cos Theta = 30.2

    is this the correct way to do this problem? Where would I go from here since I have 2 variables? any help to give me a shove would be appreciated.
    A cos(210) + 200 cos(theta) + 200 cos(65) = 250 cos(125) :: x-vectors
    A sin(210) + 200 sin(theta) + 200 sin(65) = 250 sin(125) :: y-vectors

    You have 2 unknows & 2 equations
    It is (my opinion) not a good idea to reduce the angle to first quadrant.

    .
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  3. #3
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    Quote Originally Posted by aidan View Post
    A cos(210) + 200 cos(theta) + 200 cos(65) = 250 cos(125) :: x-vectors
    A sin(210) + 200 sin(theta) + 200 sin(65) = 250 sin(125) :: y-vectors

    You have 2 unknows & 2 equations
    It is (my opinion) not a good idea to reduce the angle to first quadrant.

    .
    Thank you but I still do not know how to solve the system. I have never dealt with systems of equations involving trig functions. I went ahead and calculated the cos and sins and got this:

    -.866A + 200 cos (Theta) +84.52 = -143.39
    -1/2A + 200 sin(Theta)+181.26 = 204.8

    could someone please help me with the first few steps at least. I am not sure how to solve this.
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  4. #4
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    Quote Originally Posted by ur5pointos2slo View Post
    Thank you but I still do not know how to solve the system. I have never dealt with systems of equations involving trig functions. I went ahead and calculated the cos and sins and got this:

    -.866A + 200 cos (Theta) +84.52 = -143.39
    -1/2A + 200 sin(Theta)+181.26 = 204.8

    could someone please help me with the first few steps at least. I am not sure how to solve this.
    Let B= cos(Theta). Your equations become
    -.866A + 200 B +84.52 = -143.39
    -1/2A + 200 B+181.26 = 204.8

    or -.866A+ 200 B= -227.91
    -.5A+ 200B= 23.54
    with no trig functions! Solve for A and B and then use B= cos(THETA) so THETA= arccos(B) to find THETA.
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