题目内容


如图所示,某船上午11时30分在A处观测海岛B在北偏东60°方向,该船以每小时10海里的速度航行到C处,再观测海岛B在北偏东30°方向,又以同样的速度继续航行到D处,再观测海岛在北偏西30°方向,当轮船到达C处时恰好与海岛B相距20海里,请你确定轮船到达C处和D处的时间。



解:∵∠BAD=30°, ∠BCD=∠BDC=∠CBD=60°

    ∴△BCD为等边三角形                 

在△ABD中,∠BAD=30°, ∠BDC=60°

∴∠ABD=90°,即△ABD为直角三角形。

∵BC=20海里,

∴CD=BD=20海里。

又∵BD=AD

∴AD=40海里

∴AC=AD-CD=20海里                    


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已知:等边△ABC

(1)如图1,P为等边△ABC外一点,且∠BPC=120°.试猜想线段BP、PC、AP之间的数量关系,并证明你的猜想;
(2)如图2,P为等边△ABC内一点,且∠APD=120°.求证:PA+PD+PC>BD.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 


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