Vector problem missing magnitude of two vectors

AI Thread Summary
The discussion focuses on solving for the magnitudes of forces B and C given the resultant force and the angles of the forces involved. The user has set up equations based on the components of the forces but is struggling to find the values of B and C. It is confirmed that the user is on the right track and should use the two equations derived from the force components to solve for the unknowns. The equations provided are correct, and solving them simultaneously will yield the required magnitudes. The approach of using a system of equations is appropriate for this problem.
Hackerjack
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Homework Statement


Force A has a magnitude of 200 lb and points 35deg N of W. Force B points 40deg E of N. Force C points 30deg W of S. The resultant of the three forces has a magnitude of 260 lb and points 85deg S of W. Find the magnitude of forces B and C.

Homework Equations


A+B+C=R(resultant)
Ax+Bx+Cx=Rx
Ay+By+Cy=Ry

The Attempt at a Solution


So this is what I tried:
Ax+Bx+Cx=Rx
-200cos35 + Bsin40 - Csin30 = -260cos85
-163.8304 + Bsin40 - Csin30 = -22.6605
Bsin40 - Csin30 = 141.1699

Ay+By+Cy=Ry
200sin35 + Bcos40 - Ccos30 = -260sin85
114.7153 + Bcos40 - Ccos30 = -259.0108
Bcos40 - Ccos30 = -373.7261

This is what I tried but I still can't find the magnitude of B and C. Should I use system of equations to find B and C? Am I even on the right track?
 
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Hackerjack said:

Homework Statement


Force A has a magnitude of 200 lb and points 35deg N of W. Force B points 40deg E of N. Force C points 30deg W of S. The resultant of the three forces has a magnitude of 260 lb and points 85deg S of W. Find the magnitude of forces B and C.

Homework Equations


A+B+C=R(resultant)
Ax+Bx+Cx=Rx
Ay+By+Cy=Ry

The Attempt at a Solution


So this is what I tried:
Ax+Bx+Cx=Rx
-200cos35 + Bsin40 - Csin30 = -260cos85
-163.8304 + Bsin40 - Csin30 = -22.6605
Bsin40 - Csin30 = 141.1699

Ay+By+Cy=Ry
200sin35 + Bcos40 - Ccos30 = -260sin85
114.7153 + Bcos40 - Ccos30 = -259.0108
Bcos40 - Ccos30 = -373.7261

This is what I tried but I still can't find the magnitude of B and C. Should I use system of equations to find B and C? Am I even on the right track?
Yes, although I didn't verify that your equations are correct.
I copied these equations from your work above. There are two equations in two unknowns, so solving these equations simultaneously should give you values for B and C.
-200cos35 + Bsin40 - Csin30 = -260cos85
200sin35 + Bcos40 - Ccos30 = -260sin85
 
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