# Vector problem missing magnitude of two vectors

## 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?

Mark44
Mentor

## 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