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云南省昆明市2023~2024学年高二期末质量检测试题(数学)试卷答案
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24.Whatdoestheunderlinedword"that"inparagraph1referto?A.Duran'sskateboard.B.Duran'shobby.€500.C.Duran'sability.D.Duran'sweight.25.WhydidDuranfoundChubRollz?A.Torealizehischildhooddream.B.Tohelpplus-sizepeopleloseweight.C.Tofightfortheequalrightsforplus-sizepeople.hobby-skate-D.Tochangepeople'simpressionofplus-sizepeopleinsports.ontheskate-26.WhichwordcanbestdescribeDuran?A.Generous.edthatwastheB.Inspiring.C.Adaptable.D.Talented.27.WhichismostprobablyDuran'sbelief?In'tfindany-A.Everyonehasagiftforsports.B.Nooneistoofattoenjoysports.notbeskat-s,DuransetC.Overweightpeopleneedexercisemorethanothers.eknewthatD.Skateboardingismostsuitableforoverweightpeople.CreateasafeotakepartAkeypartofprotectingendangeredspeciesisfiguringoutwherethey'reliving.Nowresearch-alsohostederssaytheyhavefoundapowerfulnewtoolthatcouldhelp:vacuumingDNAoutoftheair.UsingenvironmentalDNA,oreDNA,totrackspeciesisn'tneoteric.Forafewyearsvedlotsofnow,researchershavebeenusingDNAinwatertotrackaquaticanimals.They'vealsobeenboarding.abletopickupeDNAfromplantsfloatingintheair.ButtheideaofusingeDNAfromairtoclothingtrackalargelandanimallikearhinocerosoragiraffestillseemed"crazy"toKristineBohm-ann,aresearcherattheGlobeInstituteattheUniversityofCopenhageninDenmark.lyimageChristinaLynggaardisapostdocinBohmann'steam.HerfirstjobwastofigureoutwhatkindofdevicetheteamcouldusetovacuumeDNAfromtheair."Wetriedthreedifferentde-amorerengthsvices,andoneofthemwasavacuumcleaner,acommercialone,"Lynggaardsays.Itworked,heavyalthoughitwas"supernoisy".Lynggaardalsousedsomehomemadesamplersthatusedasmallfan,likeacomputerblowerfan,mountedina3-Dprintedhousing.Theyworkedjustaswellandwerefarquieterandmorepowerefficient.anhasit”Tomaketheexperimentsuccessful,theteamalsoneededagoodplacetolookforanimalDNA."WerealizewearebasedinCopenhagen.WehavetheCopenhagenZoo,"Bohmannrecalls.Itseemedlikethezoowascustom-builtforthisexperiment:MostoftheanimalsareG】I77【23新高考·JD·英语-QG】1
分析（1）已知等式利用正弦定理化简，再利用两角和与差的正弦函数公式及诱导公式变形，求出tanB的值，由B为三角形的内角，利用特殊角的三角函数值即可求出B的度数；
（2）利用已知及三角形的面积公式可求ac=4$\sqrt{2}$，利用余弦定理及平方和公式整理可得：a+c=2$\sqrt{2}+2$，两式联立即可求得a，c的值．
解答解：（1）由已知及正弦定理得：sinA=sinBcosC+sinBsinC①，
∵sinA=sin（B+C）=sinBcosC+cosBsinC②，
∴sinB=cosB，即tanB=1，
∵B为三角形的内角，
∴B=$\frac{π}{4}$；
（2）∵S△ABC=$\frac{1}{2}$acsinB=$\frac{\sqrt{2}}{4}$ac=2，
∴解得：ac=4$\sqrt{2}$．①
∵由已知及余弦定理得：4=a2+c2-2accos$\frac{π}{4}$=a2+c2-$\sqrt{2}$ac=（a+c）2-2ac-$\sqrt{2}$ac=（a+c）2-8$\sqrt{2}$-8，
∴解得：（a+c）2=12+8$\sqrt{2}$，可得：a+c=2$\sqrt{2}+2$，②
∴由②可解得：a=2$\sqrt{2}+2$，代入①，整理可得：c2-（2$\sqrt{2}$+2）c+4$\sqrt{2}$=0．
∴解得：$\left\{\begin{array}{l}{c=2\sqrt{2}}\\{a=2}\end{array}\right.$或$\left\{\begin{array}{l}{c=2}\\{a=2\sqrt{2}}\end{array}\right.$．
点评此题考查了正弦、余弦定理，三角形的面积公式，两角和与差的正弦函数公式，以及平方和公式的运用，熟练掌握定理及公式是解本题的关键，属于中档题．
