Three force F,F and sqrt(2) F acting at a point are in equilibrium. Find the angles between the forces.

Three force F,F and sqrt(2) F acting at a point are in equilibrium. Fi

1.	Three force F,F and sqrt(2) F acting at a point are in equilibrium. Find the angles between the forces.
Answer» Solution :Fig. shows the THREE force. Let the angles between the forces be `alpha, BETA` and `gamma`, as shown in the figure. `:. " " alpha+beta+gamma = 360^(@)` or, `" "beta+gamma= 360^(@)-alpha` `:. "" sin (beta+gamma) = -SINALPHA` By Lami.s theorem, `(sqrt(2)F)/(sinalpha)=(F)/(sinbeta)=(F)/(singamma)` `:. " " beta=gamma` Also, `" "(F)/(sinbeta)=(sqrt2F)/(sinalpha)or, sinalpha= sqrt(2)sinbeta.` Now, `" sinalpha=-sin(beta+gamma)=-sin2beta=-2sinbetacosbeta` Hence, `-2 sinbeta cos beta= sqrt(2)sin beta` or,`"" cosbeta=-(1)/(sqrt(2))=cos 135^(@)` `:. " " beta = 135^(@)=gamma` and `" " a= 360^(@) -(135^(@)+135^(@)) = 90^(@)`.