题目

如图10-22，在正三棱柱ABC—A1B1C1中，AB=3，AA1=4，M为AA1的中点，P是BC上一点，且由P沿棱柱侧面经过棱CC1到M的最短路线长为，设这条最短路线与CC1的交点为N。   求：（1）该三棱柱侧面展开图的对角线长； （2）PC与NC的长； （3）平面NMP与平面ABC所成二面角（锐角）的大小（用反三角函数表示）。 答案：角）。在Rt△PHC中，∵∠PCH=∠PCP1=60°，∴CH=、在Rt△NCH中tan∠NHC=∠NHC=arctan∴平面NMP与平面ABC所成二面角（锐角）的大小为arctan。 解法2：∵△MPN在△ABC上的射影为△APC，设所求的角为θ则cosθ=.故平面NMP与平面ABC所成二面角（锐角）的大小为arccos.阅读理解　　  　　Some people do not like anything to be out of place, they are never late for work; they return their books to the library on time; they remember people's birthday and they pay their bills as soon as they arrive. Mr Dodds is such a person. 　　Mr Dodds works in a bank, and lives alone. The only family he has were in the next town: his sister lives there with her husband, and her son, Mark. Mr Dodds does not see his sister, or his family, from one year to the next, but he sends them Christmas cards, and he has not forgotten one of Mark's seventeen birthdays. Last week Mr Dodds had quite a surprise. He drove home from the bank at the usual time and drove neither too slowly nor too fast; he parked his car where he always parked it, out of the way of other cars, and he went inside to make his evening meal. At once, there was a knock at the door. Mr Dodds opened the door to find a policeman standing at the door.　　 　　“What have I done wrong?”Mr Dodds asked himself.“Have I driven on the wrong side of the road? Has there been some trouble at the bank? Have I forgotten to pay an important bill?”　　 　　“Hello, Uncle”said the policeman,“My name's Mark.”　　 1．Mr Dodds sees his sister ________.　　 [　　]　　 　　 　　 　　 A．very little　　 　　 B．only at Christmas time　　 　　 　　 C．only at the end of the year　　 　　 D．on Mark's birthday every year　　 　　 　　 　　 　　 　　 2．Mr Dodds ________.　　 [　　]　　 A．has forgotten more than one Mark's birthday　　 B．has not sent Mark anything on his seventeenth birthday　　 C．always sends a Christmas card on Mark's birthday　　 D．always sends Mark something on his birthday　　 3．When he heard a knock at the door, he was ________.　　 [　　]　　 　　 　　 　　 A．cooking a meal　　 　　 B．parking his car　　 　　 　　 C．at the door　　 　　 D．just beginning to cook a meal　　 　　 　　 　　 　　 　　 4．Mr Dodds was surprised that ________.　　 [　　]　　 A．a policeman visited him　　 B．Mark came to see him　　 C．he had forgotten Mark's birthday　　 D．someone was knocking at the door　　 5．Which of the following best describes the writer's attitude towards Mr Dodds? ________.　　 [　　]　　 A．Mr Dodds always insists on his opinion　　 B．Mr Dodds is not strict in his work　　 C．Mr Dodds never makes a mistake　　 D．Mr Dodds does not care about others