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

[Riazy]

Homework Statement

Calculation of the forces C and T in the figure

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

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

Homework Equations

Equations used are
Sum of Fx= 0
and Sum of Fy = 0

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 don't 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 isn't 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"

 

[SteamKing]

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.

 

[Riazy]

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?

 

[SteamKing]

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.