How can I find the resultant force using only the law of cosines and sines?

[Saladsamurai]

Homework Statement

Okay, I am only allowed to use law of cosines and sones to find the resultant force F_r

I am having a hell of a time finding a usable angle after drawing my parellelogram..so obviously I am in need of sleep.

What am I missing here? (pic is clickable)

Casey

 

[Saladsamurai]

I know I need to isolate a triangle, but I really suck at similar triangles when they are not necessarily right triangles.

 

[Doc Al]

Draw yourself a diagram where you add the vectors (head to tail addition). The two vectors are the two sides of a triangle. You should be able to identify the angle between them and apply the law of cosines to find the third side of the triangle, which will be the resultant.

 

[G01]

The 120 degree angle should be the angle corresponding to your resultant vector in the triangle. For the other angles:

HINT: What is the angle between the 80lb force and the -x axis? Does this help you find another angle in your parallelogram?

 

[Saladsamurai]

Is the angle between them by any chance 60 degrees? In the parellepgram 2(120)=240 leaving 120/2 to give me four angles that add to 360

 

[Doc Al]

Is the angle between them by any chance 60 degrees?

Yes. (Assuming you're talking about the triangle I referred to.)

 

[Saladsamurai]

I'll be back in 20 minutes. All of the theological students just showed up at StarBucks and I can't take their banter...I'm going home.

Casey

Yes. (Assuming you're talking about the triangle I referred to.)

Angle between 60 and 80 with tail of 60 at tip of 80.

 

[Doc Al]

Run for it, man!

 

[Saladsamurai]

I made it home!

Thanks Doc and G01! I am taking this Statics course over X-mass break :points gun into mouth and fake blows brains out:

So is the general approach to these to use the fact that vectors can be moved around to redraw the scenario in a manner that helps to generate more information from the given info?

Casey

 

[Doc Al]

Yes. When adding vectors, you can move them around at will as long as you keep the magnitude and direction the same.