If #h# is the height the object moves up the plane and #l# is the slant distance moved along the plane and #d# is the run.

#h/l=sintheta#

Force of friction #F_f=muN=mumg cos theta#

Where #mu# is the coefficient of dynamic friction

#m# is the mass

#g# is gravity

#theta# is the angle above horizontal

Work done against friction:

#"work done" = "force due to friction" xx "distance moved "l#

#= (muxxmgcostheta) xx l#

When the object comes to stop, part of its Kinetic energy #E# got converted into its potential energy and rest of it has been used to overcome kinetic friction.

#mgh=E- mumgcos thetaxxl#

#mglsintheta=E- mumgcos thetaxxl#, solving for #l#

#=>l =E/(mgsintheta+mumgcostheta)#

Again

#"work done" = "force due to friction" xx "distance moved "l#

#= (muxxmgcostheta) xx l#

#=(muEmgcostheta)/(mgsintheta+mumgcostheta)=
(muEcostheta)/(sintheta+mucostheta)#