++++++++++++++++++85

∵∠A=30°，∴ B到AD的距离=AB/2=20cm。∵∠DBC=75°，∴∠ADB=∠DBC-∠A=45°。用正弦定理AD=ABsin∠ABD/sin∠ADB=40sin(180°-75°)/sin45°=40*(1/4)(√6+√2)/(1/√2)=20(√3+1)cm。∴ CD=AD/2=10(√3+1)cm。