解:如圖,過點?$B$?作?$BE⊥CD$?于點?$E,$?連接?$BD$?
∵?$AB=4m,$??$C$?為?$AB$?的中點
∴?$BC=2m$?
∵?$∠BCD=60°$?
∴?$BE=sin 60°×BC=\sqrt 3,$??$CE=cos 60°×BC=1$?
設(shè)?$DE=x$?
?$CD=x+1,$??$BD=x+1-0.5=x+0.5$?
∵?$BE^2+DE^2=BD^2$?
∴?$x^2+(\sqrt 3)^2=(x+0.5)^2$?
?$x=2.75$?
?$CD=x+1=3.75m$?