题目

（7分）如图，南京绿博园中有一条人工河，河的两岸PQ、MN互相平行，河岸PQ上有一排间隔为50米的彩灯柱C、D、E、……，某人在河岸MN的A处测得∠DAN＝21º，然后沿河岸走了175米到达B处，测得∠CBN＝45º，求这条河的宽度．（参考数据：，）    答案：作AS⊥PQ，CT⊥MN，垂足分别为S，T．由题意知，四边形ATCS为矩形，所以AS=CT，SC=AT．设这条河的宽度为x米．在Rt△ADS中，因为，所以．······················································（2分）在Rt△BCT中，因为，所以．                  ······················································（3分）因为SD+DC =AB+BT，所以，···············································（6分）解得，即这条河的宽度为75米． ······················································（7分）（其它方法相应给分）解析:略 

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