题目

如图,在四棱锥P—ABCD中,底面ABCD是直角梯形, BC∥AD,且∠BAD=90°,又PA⊥底面ABCD,BC=AB=PA=1,AD=2.(1)求二面角P-CD-A的平面角的正弦值;(2)求A到平面PCD的距离. 答案：解:(1)在四棱锥P—ABCD中,底面ABCD是直角梯形,且BC∥AD,∠BAD=90°,连结AC,而AB=BC=1,则AC=,又AD=2,∠CAD=,由余弦定理可求得CD=.故AC⊥CD.又PA⊥面ABCD,∴AC为PC在面ABCD内的射影.∴CD⊥PC.∴∠PCA是二面角P-CD-A的平面角.又PA=1,AC=,则PC=,故sin∠PCA=. (2)由(1)可知DC⊥面PAC,∴面PAC⊥面PCD.过A作AH⊥PC于H,则AH⊥PC,故AH为A点到平面PCD之短文改错假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。文中共有10处语言错误，每句中最多有两处。每处错误仅涉及一个单词的增加、删除或修改。增加：在缺词处加一个漏字符号(∧)，并在其下面写出该加的词。删除：把多余的词用斜线(\)划掉。修改：在错的词下画一横线，并在该词下面写出修改后的词。注意：1. 每处错误及其修改均仅限一词；2. 只允许修改10处，多者(从第11处起)不计分。In the end of the last term, I got a C in the English examination. When I knew the result, I wouldn't hold back my tear. My mood was terrible and I thought the world was coming to end. So after a while, I found I was wrong for I came to realize “Failure is the mother of success”. What I should do it was to find the reason that I got so bad a result. And I think this was a lesson to me and it helped me to find my shortcomings. Maybe it could help me to improving my English. So my bad mood turned into a better one.