如图是一台起重机的示意图，它的机身AM高为20.5米，吊杠与水平方向的倾角可以从30°转到80°，这台起重机工作的最大高度为BD=56.6米，求：吊杠AB的长是多少米

One afternoon, Kate and her brother Bob went out to play.Kate was eight, and Bob was ten.“Let’s go to the bridge and we can see fish in the river.” said Kate.
“I don’t know…” Bob said.“Mum told us, ‘don’t go on the bridge.’ She said it’s dangerous.”
Kate said, “I am not afraid.Are you?”
They walked onto the bridge and began looking for fish in the river.The bridge was a train bridge.Trains went over the bridge three times a day.
The children were standing in the middle of the bridge when they heard a loud noise.“A train is coming!” Bob shouted.“Run!” He ran to the end of the bridge.He was safe.
Kate ran, too, but she fell.The train was coming fast.Kate ran towards Bob.She fell again right on the train tracks(铁轨).There was no time to leave.She had to lie down between the tracks.A few seconds later, the train went over the girl, but she was not hurt at all.She stood up and said to Bob, “Don’t tell Mum! Don’t tell Mum!”
At last their mother found out about the story.She was angry because they went on the bridge.But she was happy that Kate was all right.
【小题1】 Bob and Kate were .A．twinsB．brothersC．sistersD．brother and sister【小题2】One afternoon they went to the bridge to see .A．their motherB．fishC．the trainD．the river【小题3】When the train came, the children were .A．in the middle of the bridgeB．at the end of the bridgeC．on their way to the bridgeD．away from the bridge【小题4】Where was Kate when the train was going over her?A．She fell again right on the train tracks(铁轨).B．Kate ran towards Bob.C．She had to lie down between the tracks.D．She stood up and cried.【小题5】When their mother knew about the story, she was .A．happyB．angryC．sorryD．both angry and happyD

(答案→)D 解析：本文讲述了鲍勃和妹妹凯特不听妈妈的话去火车桥上，结果火车来了，由于凯特跌倒，她急中生智躺在两个铁轨中间，从而躲过火车的故事。【小题1】根据Kate and her brother Bob可知，凯特和鲍勃是兄妹。所以本题选D。【小题2】根据Let’s go to the bridge and we can see fish可知，他们是为了看鱼。所以本题选B。【小题3】根据The children were standing in the middle of the bridge when they heard a loud noise.可知，火车来时，他们在桥中间。所以本题选A。【小题4】根据She had to lie down between the tracks.可知，当火车经过时，凯特躺在了铁轨中间。所以本题选C。【小题5】根据最后一段中的She was angry和she was happy 可知，他们的妈妈既高兴有生气。所以本题选D。

回答的不错

我明天再问问老师，叫他解释下这个问题

解：在Rt△ABC中，当∠BAC=80°时，BA=BC÷sin80°=（BD-CD）sin80°=（56.6-20.5）×0.9848≈30.6（米）；
在Rt△AB′C′中，当∠B′AC′=30°时，AC′=AB′?cos30°=30.6×0.866≈26.5米．
故吊杠AB的长是30.6米，最远水平距离AC′是26.5米．解析分析：当起重机起吊的高度最大时，△ABC的∠BAC=80°；当起重机位置不变时水平距离最大时，∠B′AC′=30°，根据三角函数即可求解．点评：本题考查了解直角三角形的应用，正确理解起重机起吊的高度最大，以及水平距离最大的条件是解决本题的关键．