F1cosA+F2cosB+F3cosC=0……(1)
F1sinA+F2sinB+F3sinC=0……(2)
F1sinA-F2sinB-1.575F3cosC=0……(3)
(1)×1.575+(3):
F1(sinA+1.575cosA)-F2(sinB-1.575cosB)=0
F1√(1+1.575^2)sin(A+arccot1.575)-F2√(1+1.575^2)sin(B-arccot1.575)=0
F1sin(A+arccot1.575)-F2sin(B-arccot1.575)=0……(4)
由(2)、(3):
sinC=-(F1sinA+F2sinB)/F3
cosC=(F1sinA-F2sinB)/(1.575F3)
因(sinC)^2+(sinC)^2=1
所以
(1+1.575^2)(F1)^2(sinA)^2+(1+1.575^2)(F2)^2(sinB)^2+2(-1+1.575^2)(F1F2sinAsinB=(1.575F3)^2
(F1)^2(sinA)^2+(F2)^2(sinB)^2+0.851F1F2sinAsinB=0.713(F3)^2……(5)
无法求