Solving for F3 Magnitude and Theta Given F1 and F2

[quantum_enhan]

The three concurrent forces acting on the post produce a resultant force of 0. If F2 = 0.5F1, and F1 is to be 90 degrees from F2 as shown, determine the required magnitude F3 expressed in terms of F1 and the angle theta.


I am having no troubles finding the magnitude of F3, however, I am having trouble understanding how to get theta. Apparently the angle formed by F1 and F2, plus ninety degress, gives you the answer. However, I'm not seeing the relationship. Help?

 

[Doc Al]

Use theta to find the angle that F2 (and F1) makes with the horizontal.

 

[quantum_enhan]

Wouldnt you want to find the angle that F2 (and F1) makes with the vertical, then add 90 degrees to find theta?

 

[Doc Al]

Wouldnt you want to find the angle that F2 (and F1) makes with the vertical, then add 90 degrees to find theta?

That also would work. Give it a try.

Express the angle that F1 and F2 make with the vertical or the horizontal in terms of theta. Then you can solve for theta.

 

[zgozvrm]

For the vectors to cancel out, the combination of F1 and F2 must result in a vector having the same magnitude as F3 but having opposite direction.

So, to start, find the x-components of F1 and F2. Add them together to get the magnitude of F3. Then substitute what you know about the angles.