Answer:
[tex]F_y=51.67\ N\\F=100.33\ N[/tex]
Step-by-step explanation:
The Force Vector
Like all vectors, the force has a magnitude and a direction, expressed as an angle. Let F be the magnitude of the force and [tex]\theta[/tex] the angle it forms with the positive reference. The horizontal component of the force is
[tex]F_x=F.cos\theta[/tex]
And the vertical component is
[tex]F_y=F.sin\theta[/tex]
Knowing the horizontal component is 86 Newtons and the angle is 31 degrees, we can solve the first equation for F
[tex]\displaystyle F=\frac{F_x}{cos\theta}=\frac{86}{cos31^o}[/tex]
[tex]F=100.33\ N[/tex]
Now we compute the vertical component
[tex]F_y=100.33.sin31^o=51.67[/tex]
[tex]\boxed{F_y=51.67\ N}[/tex]
