试题分析:首先过点D作DE∥AC交BC的延长线于点E,过点D作DF⊥BC于点F,易得四边形ACED是平行四边形,DE⊥BD,又由BC=5,AD=3,∠DBC=30°,即可求得BE,DE,BD的长,又由直角三角形的面积,即可得 ,则可求得答案. 过点D作DE∥AC交BC的延长线于点E,过点D作DF⊥BC于点F,
![](http://img.shitiku.com.cn/uploads/allimg/20191029/20191029075732-46468.png) ∵AD∥BC, ∴四边形ACED是平行四边形, ∴CE=AD=3, ∵AC⊥BD, ∴DE⊥BD, ∵BC=5, ∴BE=BC+CE=5+3=8, ∵∠DBC=30°, ∴DE= BE=4,
![](http://img.shitiku.com.cn/uploads/allimg/20191029/20191029075733-44673.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191029/20191029075733-91822.png) 点评:此题难度适中,注意掌握辅助线的作法,注意数形结合思想的应用. |