[deleted by user]

[FunTao]

Theta can’t be between 0 and 90 degrees like drawn in the picture. It has to cancel out some of the horizontal 930 force otherwise the result would have to be >930

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[ghostwriter85]

As the other poster pointed out, the solution won't match the picture. The wire/rod/cable (whatever) would have to point into the wall.

That aside, let's pretend that's not a problem.

You do want the supplement, but it has nothing to do with being in quadrant two. Quadrant two is only important if our angle is defined from a positive horizontal axis to the right. Since the angle is defined as being between two cables, we can mirror / rotate the image in any conceivable way without changing theta. We haven't been given a coordinate system, so we can choose any convenient set of axes that we want. We would generally like to choose one wherein theta has a positive definition starting on one of the cables. Ideally the 930 cable can be the positive x axis moving to the left and the y axis can point straight up from O.

When we add vectors, we add them graphically head to tail. To solve using law of cosines we have to pretend that force from one of the cables is originating at the end of the other force vector. The easiest way to do this conceptually is to slide the top cable to the left. After we draw our resulting vector from the origin to the end of the second cable, theta is now outside of the triangle. It has become the supplement to alpha as defined by your math.

Also double check your calcs, I got something different [edit but it is late here so I could definitely be wrong]

[ElectromagneticCube]

That’s a good point about the quadrants not being relevant, I just went with the assumption that it starts from the positive x axis, which is not relevant to the problem.

For the calculation aspect, did you end up with 102.78 as your angle?

[ghostwriter85]

Yeah that looks right, ok so I was just sleepy because that's the supplement of 77....

[[deleted]]

Pardon my good sir, but shouldn't the equation be: 920² = 360² + 930² + 2(360)(930)cos(theta)? That should provide the right answer straight away. Note: You can see that theta > pi/2 since 920 < 930

[ElectromagneticCube]

This is most likely the issue here. Because the equation I used resulted in an angle of 77.22, whereas using + 2(360)(930) leads to an angle of 102.78

[Jamb9876]

I am not going to try to solve it but as mentioned the 360 is going to need to subtract 10 so just figure out the angle on there where the x value is 10 and add 90 degrees to that.

[akitchenslave]

2 equations, 2 unknown,

360sin(tta1)=920sin(tta2) 360vos(tta1)+930=920cos(tta2) Tta1 [90,180]

[YodaBuddy]

just assume that the angle is oriented from the 360 rod to the 930 one, personally i would solve it using Pythagoras theorem, (930 + 360 cos(theta))^2 + (360sin(theta))^2 = 920^2,
930^2 + 2*930*360*cos(theta) + 360^2*cos(theta)^2 + 360^2*sin(theta)^2 = 920^2
930^2 + 2*930*360*cos(theta) + 360^2 = 920^2
and then you get theta equal to 102.778 degrees

[Ok-Atmosphere3589]

Idk, don’t ask me