Finding the angle for force component

[TheShehanigan]

Homework Statement

Find the Fx' and Fy components of the given force, given that y' is 10 degrees, there is a 60 degree angle between F and X in the negative direction, and F = 360 N. Use only the Law of Sines, Law of Cosines and Law of Parallelograms.

Homework Equations

Sin a / A = Sin b / B

C^2 = A^2 + B^2 - 2 AB Cos c

Law of Parallelograms for Vectors

The Attempt at a Solution

I've found so far a nice triangle, the one that covers the positive X axis, but I am having trouble finding Phi (which is supposed to be 10). If I can find Phi, I can solve for the components, which I know how to do. Problem is, I'm not told x' and y' are perpendicular, so I can solve using 90 degrees, or anything. I just have the 30 degrees on the bottom, and the 60 + Phi on the top left, but I'm missing the top right. Any tips on finding Phi?

Here's a pic.

 

[LCKurtz]

Could you give the exact statement of the original problem? I suppose the black lines are perpendicular x and y axes, but you haven't labeled them. And you haven't said what x' and y' are nor are they labeled. My guess is that they represent a rotation of the x and y axes through 10 degrees. I would also guess that you have the F vector pointed in the opposite direction if the angle between F and the x-axis is -60 degrees.

Please state the problem, word for word, from where you got it.

 

[Architeuthis Dux]

I commend your use of the appropriate equations and your method of approaching the problem. It seems like you have a good understanding of the concepts involved.

To find Phi, you can use the Law of Cosines equation: C^2 = A^2 + B^2 - 2ABcosC. In this case, C is the side opposite to the angle Phi, A is the side opposite to the angle 60 degrees, and B is the side opposite to the angle 30 degrees. You know the values of A and B, and you can find the value of C using the given force F = 360 N. Once you have C, you can solve for cosC and then use inverse cosine to find the value of Phi.

Alternatively, you can also use the Law of Sines equation: Sin a / A = Sin b / B. In this case, a is the angle 60 + Phi, A is the side opposite to this angle, and b is the angle 30 degrees. You know the values of A and b, so you can solve for sin a. Then, you can use inverse sine to find the value of a, which is 60 + Phi. From there, you can solve for Phi.

I hope this helps you in finding the angle Phi and solving the problem. Keep up the good work!