# Finding 2 of 3 Forces Given 1 and a Resultant

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1. Aug 22, 2015

1. The problem statement, all variables and given/known data
Force A has a magnitude of 200lb and points 35° N of W. Force B points 40° E of N. Force C points 30° W of S. The resultant of the three forces has a magnitude of 260lb and points 85° S of W.
(a) What is the magnitude of Force B?
(B) What is the magnitude of Force C?

2. Relevant equations
F = √(Fx2 + Fy2)
Fx = FcosΘ
Fy = FsinΘ

where

F = Force
Θ =Angle

3. The attempt at a solution
Having drawn these vectors, I've been trying to use components which could've been easier if 2 forces were given.

Resultant's X = Rx = 260cos85°
Resultant's Y = Ry = 260sin85°
Force A's X = Ax = 200cos35°
Force A's Y = Ay = 200sin35°
Bx = Bsin40°
By = Bcos40°
Cx = Csin30°
Cy = Ccos30°
And formed equations

R = A + B + C
Rx = Acos35° + Bx + Cx
Ry = Asin35° + By + Cy
With these, I don't really know because 2 are missing while having no other equations for them like A+B=1 or stuff like that that give hints. Seems like something is missing, but i don't know because others have solved it. Don't know what is next.

2. Aug 22, 2015

### BvU

Hello cad, welcome to PF !

You have two unknows (B and C) and two equations.
You are making life difficult for yourself by dragging in Bx, y and Cx, y.

By the way, I hope you don't mean R = A + B + C but $\vec R = \vec A + \vec B + \vec C$

Last edited: Aug 22, 2015
3. Aug 22, 2015

So 260 = 200 + $\vec B + \vec C$ would be the first equation and i'll have to find the other equation
By any chance, does the 2nd equation contain angles in it? Or anything?

4. Aug 23, 2015

### BvU

260 and 200 are not vectors. I take it you do know about vector addition ?

You have two equations

with two unknowns: the magnitudes B and C.​

Perhaps I confused you with my blunt comment
but the intention was that you would substitue the magnitudes of B and C

5. Aug 23, 2015

I see. I came up with estimated answers B = 1780.15 and C = 2006.18. I also checked and resulted to 259.99... Am I doing this right?

6. Aug 23, 2015

### BvU

Does it match with the drawing you mentioned in post #1 ?

7. Aug 24, 2015

### BvU

Check your angles. Do they have the same reference ?
In math and physics, east is zero angle, north $\pi/2$

8. Aug 24, 2015

### BvU

Never mind, it matches. Note that finding the magnitude of $\vec A + \vec B + \vec C$ is 260 is not enough to ensure $\vec R = \vec A + \vec B + \vec C$; the direction has to be the same too.
But from you answer I expect you did the right thing and equated x and y components. WEll done.

9. Aug 27, 2015

### Mystery

Hi, im a newbie here... can someone explain how did he got the values of B and C??

10. Aug 27, 2015

### Mystery

how did you got B and C??