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Question (with solution) which I don't understand (statics)

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculation of the forces C and T in the figure

    http://www.picpaste.com/20140127_171733-lxIN0kJQ.jpg [Broken]
    http://www.picpaste.com/20140127_171733-lxIN0kJQ.jpg [Broken]

    My problem is that I don't understand how cos and sin is given
    I know the rules SOHCAHTOA



    2. Relevant equations
    Equations used are
    Sum of Fx= 0
    and Sum of Fy = 0


    3. The attempt at a solution

    As this is an example from my coursework material, it is already solved. But I want to understand it there for I will present the solution

    Sum of Fx = 0

    8+Tcos40 + Csin20 - 16 = 0
    0,766T+0,342C=8

    Sum of Fy = 0

    Tsin40-Ccos20-3=0
    0,643T-0,940C = 3

    By combining the both equations we can solve for C and T

    Answer is T = 9,09 kn and C = 3,03 kn

    So basically my question is how are cos and sin given? yeah i know its a triangle
    and I know of SOH CAH TOA rule.. but i dont seem to grasp it when in this Picture

    Actually as I am used to see a problem I first

    draw a triangle for example for the 40 degree one, sometimes i divide a resultant force into two composants

    I see that T = hypotenuse
    Then I look at the adjacent side, and normally there is a variable there which is present without a value that I want to be solved.. Now in this problem 8 isnt used as a value. Normally I would divide T into Tx and Ty, and draw to triangles.


    So how should I look at this problem now?

    how do i know its sin i will use respectively cos... if someone could explain it It would be very kind of you . how should I Think? B]

    I Believe in this problem I am not supposed to divide into two composants, but i want to know how they decide "when to use cos resp sin"
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 27, 2014 #2

    SteamKing

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    You have to master which side of the angle is adjacent to the angle and which is opposite the angle.

    For vector T, the adjacent side of the 40 degree angle is the x-axis, so the horizontal component is T cos 40.

    For vector C, the adjacent side of the 20 degree angle is the y-axis, so the vertical component is C cos 20.
     
  4. Jan 27, 2014 #3
    Sum of Fx = 0

    8+Tcos40 + Csin20 - 16 = 0
    0,766T+0,342C=8

    Sum of Fy = 0

    Tsin40-Ccos20-3=0
    0,643T-0,940C = 3


    could you show me somehow?
     
  5. Jan 27, 2014 #4

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Draw out the triangles on the diagram. That way, you will be able to see how the sin and cos relationships correspond to the horizontal and vertical components of the different vectors.
     
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