The force applied to the box will be balanced by the component of weight which can be expressed as,
[tex]F=W\sin \theta[/tex]Substitute the known values in the equation,
[tex]\begin{gathered} 20\text{ N=(50 N)sin}\theta \\ \sin \theta=\frac{20\text{ N}}{50\text{ N}} \\ \theta=\sin ^{-1}(0.4) \\ \approx23.6^{\circ} \end{gathered}[/tex]The height of the ramp can be given as,
[tex]h=d\sin \theta[/tex]Substitute the known values,
[tex]\begin{gathered} h=(10m)sin23.6^{\circ} \\ =(10\text{ m)(}0.4) \\ =4\text{ m} \end{gathered}[/tex]Thus, the height of the ramp is 4 m.
