We know that
• The force is 16 Newtons.
,• The angle of application is 71 degrees.
,• The box weighs 15 Newtons.
First, let's make a free-body diagram.
As you can observe, the vertical vectors are the weight of the box and the vertical component of the applied force.
[tex]\Sigma F_y=F_y-W[/tex]Where each force is defined as follows
[tex]\begin{gathered} F_y=F\cdot\sin \theta \\ W=mg \end{gathered}[/tex]Let's use the expressions above to find the net vertical force.
[tex]\begin{gathered} \Sigma F_y=F\cdot\sin \theta-mg=16N\cdot\sin 71-15 \\ \Sigma F_y\approx0.13N \end{gathered}[/tex]
