Question

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

（1）請(qǐng)根據(jù)以上描述，畫(huà)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(jìn)，是否有被淺灘阻礙的危險(xiǎn)？為什么？                                                                       

                                                                     

Answer 1

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

【專(zhuān)題】計(jì)算題；壓軸題．                                                                     

【分析】先根據(jù)題意畫(huà)圖，作CD⊥直線(xiàn)AB于點(diǎn)D，根據(jù)已知求得CD的長(zhǎng)再與120比較，若大于120則無(wú)危險(xiǎn)，反之有危險(xiǎn)．                                                                                                   

【解答】解：（1）                                                                            

                                                                     

                                                                                                          

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

作CD⊥直線(xiàn)AB于點(diǎn)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(jìn)沒(méi)有被淺灘阻礙的危險(xiǎn)．                                             

【點(diǎn)評(píng)】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．