题目

A，B两地被大山阻隔，若要从A地到B地，只能沿着如图所示的公路先从A地到C地，再由C地到B地．现计划开凿隧道A，B两地直线贯通，经测量得：∠CAB=30°，∠CBA=45°，AC=20km，求隧道开通后与隧道开通前相比，从A地到B地的路程将缩短多少？（结果精确到0.1km，参考数据： ≈1.414， ≈1.732） 答案：解：过点C作CD⊥AB与D，∵AC=10km，∠CAB=30°，∴CD= 12 AC= 12 ×20=10km，AD=cos∠CAB•AC=cos∠30°×20=10 3 km，∵∠CBA=45°，∴BD=CD=10km，BC= 2 CD=10 2 ≈14.14km，∴AB=AD+BD=10 3 +10≈27.32km，则AC+BC﹣AB≈20+14.14﹣27.32≈6.8km，答：从A地到B地的路程将缩短6.8km( B ) 8. —Excuse me，can you tell me_?—Sorry, I don’t know. You can go to the information desk.A. that there is a planeB. when the plane takes offC. which plane can I takeD. where does the plane fly