The torque is defined as:
[tex]\tau = F d \sin \theta[/tex]
where
F is the force applied
d is the distance of the arm
[tex]\theta[/tex] is the angle between the direction of the force and the arm
In this problem, the torque required must be [tex]\tau=89 Nm[/tex], the length of the arm (the lug wrench) is [tex]d=0.25 m[/tex] and the angle between the force and the wrench is [tex]\theta=52^{\circ}[/tex], therefore we can find the magnitude of the force by re-arranging the previous equation and by plugging these data into it:
[tex]F= \frac{\tau}{d \sin \theta}= \frac{89 Nm}{(0.25 m)(\sin 52^{\circ})}=451.8 N [/tex]
