Answer
$F_a=30.6lb$
$F_b=26.9lb$
Work Step by Step
We are given that the force acting on the gear tooth is $F=20lb$.
Using the law of sines with the given angles, we can resolve the F into it's components.
$\sin40^{\circ} / 20lb = \sin 80^{\circ} / F_a$
Solving for $F_a$, we obtain:
$F_a=30.6lb$
$\sin40^{\circ} / 20lb = \sin 60^{\circ} / F_b$
Solving for $F_b$, we obtain:
$F_b=26.9lb$
