Resolving forces and finding from the resultant

[mm391]

Homework Statement

Three forces: F1, F2 and the other with a magnitude of 40 N act on the ring bolt as shown in Fig. C.1. The resultant, R, has a magnitude of R = 180 N and acts at an angle of 80° anti-clockwise from the x-axis. Determine the magnitudes of F1 and F2.

Homework Equations

ƩF_x
ƩF_y

The Attempt at a Solution

ƩF_x=F2*cos(40)-F1cos(60)=180*cos(80)
ƩF_y=F1*sin(40)+40+F2*sin(40)=18-*sin(80)

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[tiny-tim]

hi mm391!

ƩF_x=F2*cos(40)-F1cos(60)=180*cos(80)
ƩF_y=F1*sin(60)+40+F2*sin(40)=180*sin(80)

two equations, two unknowns …

eliminate one unknown and solve ​