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## Homework Statement

I know how to find the resultant or a force if I have been given 1 or 2 or 3 forces etc. Or find a force if I have been given the resultant. However in my textbook there was nothing on a situation where I need to find F2 and F3 if I have been given FR and F1 right?

My question is:

A hook has been subjected to three forces (F1,F2,F3). FR (resultant) = 150kN and its angle from positive x-axis is 60.

F1 = 35kN & angle is 180 from positive x axis.

Calculate magnitude of F2 and F3.

(F2 angle = 135 and F3 angle = 30)

## Homework Equations

## The Attempt at a Solution

Where I was going with it:

I thought i would write two equations summing the x and y components and then use simultaneous equations to solve..

Sum of x-components:

(35kN)cos(180) + (F2)cos(135) + (F3)cos(30) = (150kN)cos(60)

Sum of y-components:

(35kN)sin(180) + (F2)sin(135) + (F3)sin(30) = (150kN)sin(60)

Then I got to this point and thought, geez, i havn't used simultaneous equations in god knows how long... Didn't really know where to go from here. If anyone can help explain simultaneous equations to this particular problem that would be amazing!

Or, better yet if I went about my initial attempt completely wrong.. then please let me know. Thankyou in advance!