Help with vector algebra getting an undefined answer

[HeJind]

Homework Statement

Determine the magnitude of F that will cause the net effect of
the three forces to act vertically.

In the diagram there are three bolts (I'll refer to the first two as B1 and B2), and the third bolt, F, is undefined. F acts 45 degrees northeast of the horizontal, B1 is 410N and acts 30 degrees west of north, and B2 is 200N and acts 10 degrees north of west.

The Attempt at a Solution

I used vector algebra to set up the equation, diving what vetors into x & y components. The net force in the x direction would be equivalent to -410cos(30) - 200cos(10) + "F"cos(45), and the net Y would be 410sin(30) + 200sin(40) + "F"sin(45).

adding the squares of X & Y and taking the square root of the sum would obviously give me the resultant. However, here's where I run into a problem.

When I set up the equation to show that the net force was acting vertically, I got 90 = arctan(Ry/Rx) . This would mean that Ry/Rx = Tan(90) but tan90 is obviously undefined. What am I doing wrong?

 

[jedishrfu]

If its acting vertically then what would the x component of the resultant force be?

 

[HeJind]

Ah...makes sense now. I greatly over complicated this problem. Thank you!