How to Numerically Solve for a Fourth Force to Achieve a Specific Resultant?

[twofish]

Homework Statement

First of all I will have to apologize if this in in the wrong forum. It is a 1st year engineering mechanics problem.

I am having an issue solving a secondary part of a question.
The first part of the question has asked me to both graphically and numerically determine a resultant of three forces acting on an object, with magnitude and angles for all given. This was straightforward.
I am now being asked to determine a fourth Force such that the resultant R of all the four forces will be vertical (90 degrees) and has a magnitude of 750 N.
I have done this question graphically, but am wondering how I go about doing it numerically ..just buy using trig etc.
thanks much,

The Attempt at a Solution

i have thus far determined that my previous resultant force was 821 N at 87 degrees North of East.
I have therefore now said that my resultant is going to have to = 750 N so
750 = (sum Fx + sum Fy)^(1/2).
I am just unsure how I would go about getting two unkowns from this methodology, the X component and Y component of the unkown vector..

 

[learningphysics]

What is the x - component of your 821N force ? Add to that and the x-component of your new force and you get 0. solve for the x-component of the new force.

same way, solve for the y-component.

 

[twofish]

Well the last resultant at a magnitude of 821N had 50.0007N (X-component) and 819.181N (Y component). Direction was 86.5 degrees N of E
Now I need to add a Force such the new resultant will be 750N and vertical (or 90 degrees).
I guess what I am saying is, I don't know how to get the X or Y component for my new force, becuase I don't know what it will be.

 

[learningphysics]

50.0007N + Fx = 0, solve for Fx

819.181N + Fy = 750, solve for Fy.

 

[twofish]

of course.. how silly of me, I was trying to make a triangle and use law of cosines.. thanks much!