解:?$ (1)$?過點(diǎn)?$F $?作?$FH⊥CD$?交于點(diǎn)?$H$?
∵?$∠CDF=30°$?
∴?$FH=DF×sin 30°=15\ \mathrm {cm},$?
?$DH=cos 30°×DF=15\sqrt{3}\ \mathrm {cm}$?
∵?$∠DCF=45°$?
∴?$CH=FH= 15\ \mathrm {cm}$?
∴?$CD= CH+ DH= (15 + 15\sqrt{3})\ \mathrm {cm}$?
∵?$CE :$??$ CD= 1:$??$3$?
∴?$CE= (5+5\sqrt{3})\ \mathrm {cm}$?
∴?$DE= CE+CD= (20+20\sqrt{3})\ \mathrm {cm}$?
∵?$DE= BC= AB$?
∴?$AC= 2DE= (40 + 40\sqrt{3})\ \mathrm {cm}$?
?$(2)$?過點(diǎn)?$A$?作?$AG⊥DE$?于點(diǎn)?$G$?
∵?$∠ACD=45°$?
∴?$AG= sin 45°×AC= 20\sqrt{2}+20\sqrt{6}≈77\ \mathrm {cm}$?
答:拉桿端點(diǎn)?$A$?到水平滑桿?$DE$?的距離是?$77\ \mathrm {cm}。$?