Question

一條船在海面上自西向東沿直線航行，在A處測得航標(biāo)C在北偏東60°方向上，前進100米到達B處，又測得航標(biāo)C在北偏東45°方向上．                                                                                  

（1）請根據(jù)以上描述，畫出圖形．                                                         

（2）已知以航標(biāo)C為圓心，120米為半徑的圓形區(qū)域內(nèi)有淺灘，若這條船繼續(xù)前進，是否有被淺灘阻礙的危險？為什么？                                                                       

                                                                     

Answer 1

【考點】解直角三角形的應(yīng)用-方向角問題．                                           

【專題】計算題；壓軸題．                                                                     

【分析】先根據(jù)題意畫圖，作CD⊥直線AB于點D，根據(jù)已知求得CD的長再與120比較，若大于120則無危險，反之有危險．                                                                                                   

【解答】解：（1）                                                                            

                                                                     

                                                                                                          

（2）答：這條船繼續(xù)前進，沒有被淺灘阻礙的危險．                                    

作CD⊥直線AB于點D，                                                                        

由已知可得∠CAD=30°，∠CBD=45°，                                                    

AB=100米．                                                                                      

設(shè)CD=x米．                                                                                     

在Rt△ACD中，tan∠CAD=，                                                             

∴AD=，                                                               

在Rt△CBD中，∵∠CBD=45°，                                                             

∴BD=CD=x，                                                                                    

∵AD﹣BD=AB，                                                                                

∴，                                                                             

解得，                                                                       

∴這條船繼續(xù)前進沒有被淺灘阻礙的危險．                                             

【點評】此題考查學(xué)生基本的作圖能力，及構(gòu)造直角三角形解題的能力．