初中三角函数知识点总结及中考真题讲解

初中三角函数知识点总结及中考真题讲解锐角三角函数知识点总结222b1、勾股定理:直角三角形两直角边、的平方和等于斜边的平方。a，b,cac2、如下图，在Rt?ABC中，?C为直角，则?A的锐角三角函数为(?A可换成?B):定义表达式取值范围关系a0,sinA,1正，A的对边sinA,cosBsinA,sinA,c弦(?A为锐角)斜边cosA,sinB22b0,cosA,1余，A的邻边sinA，cosA,1cosA,cosA,c弦(?A为锐角)斜边tanA,cotBatanA,0正，A的对边tanA,tanA,cotA,tanBb切(?A为锐角)，A的邻边1(倒数)tanA,cotAbcotA,0余，A的邻边cotA,cotA,tanA,cotA,1a切(?A为锐角)，A的对边3、任意锐角的正弦值等于它的余角的余弦值;任意锐角的余弦值等于它的余角的正弦值。BsinA,cosB由，A，，B,90:sinA,cos(90:,A)对斜边cosA,sinBcosA,sin(90:,A)得，B,90:,，Ac边abAC邻边4、任意锐角的正切值等于它的余角的余切值;任意锐角的余切值等于它的余角的正切值。tanA,cotBtanA,cot(90:,A)由，A，，B,90:cotA,tanBcotA,tan(90:,A)得，B,90:,，A5、0?、30?、45?、60?、90?特殊角的三角函数值(重要)三角函数30?45?60?213sin,222213cos,2223tan,3136、正弦、余弦的增减性:,,,,,当0???90?时，sin随的增大而增大，cos随的增大而减小。7、正切、余切的增减性:,,,,,当0?<<90?时，tan随的增大而增大，cot随的增大而减小。8、解直角三角形的定义:已知边和角(两个，其中必有一边)?所有未知的边和角。222依据:?边的关系:;?角的关系:A+B=90?;?边角关系:三角函数的定义。(注意:尽量避a，b,c免使用中间数据和除法)geographiclocationYibincityislocatedinbeautifulrichof"abundance"--SichuanbasinSouthmargin,islocatedinn103?39'-105?20',latitude27?49'-29?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyearsplanningplatformforintoYucityintertracknetworkplanning(2011-2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdblockingspecialplanningYibincityrelatedtabletsdistrictcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibincityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiverandYangtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovincecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxi-liupanshui"importantpartoftheresource-richregion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuan-Yunnan-Guizhou-basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCounty,xingwenjunlian,andGong,and,and,and.2.1-2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulationof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibincity,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovince-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-scaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsocialretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofurbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Wine-makingindustry,9、应用举例:(1)仰角:视线在水平线上方的角;俯角:视线在水平线下方的角。视线铅垂线水平线仰角ihl,:h俯角α视线lhhl1:mi,(2)坡面的铅直高度和水平宽度的比叫做坡度(坡比)。用字母表示，即。坡度一般写成的形式，ili,1:5如等。h把坡面与水平面的夹角记作(叫做坡角)，那么i,,tan,。,l3、从某点的指北方向按顺时针转到目标方向的水平角，叫做方位角。如图3，OA、OB、OC、OD的方向角分别是:45?、135?、225?。4、指北或指南方向线与目标方向线所成的小于90?的水平角，叫做方向角。如图4,OA、OB、OC、OD的方向角分别是:北偏东30?(东北方向)，南偏东45?(东南方向)，南偏西60?(西南方向)，北偏西60?(西北方向)。要点一:锐角三角函数的基本概念一、选择题ion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuanrichreg-liupanshui"importantpartoftheresource-cecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxigtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovinndYancityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiveractcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibinockingspecialplanningYibincityrelatedtabletsdistri2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdbl-rsplanningplatformforintoYucityintertracknetworkplanning(201129?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyea-105?20',latitude27?49'-SichuanbasinSouthmargin,islocatedinn103?39'--cationYibincityislocatedinbeautifulrichof"abundance"geographiclo2makingindustry,-rbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Winealretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofuscaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsoci-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-city,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovinceionof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibin2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulat-unty,xingwenjunlian,andGong,and,and,and.2.1basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCo-Guizhou-Yunnan-1.(2009?漳州中考)三角形在方格纸中的位置如图所示，则tan,的值是()3434A(B(C(D(534512.(2008?威海中考)在?ABC中，?C,90?，tanA,，则sinB,()32310310A(B(C(D(341010?O?O?O?ABC3.(2009?齐齐哈尔中考)如图，是的外接圆，是的直径，若的半径AD3AC,2sinB为，，则的值是()22334A(B(C(D(3243Rt?ABC，,ACBRt，BC,1AB,24.(2009?湖州中考)如图，在中，，，，则下列结论正确的是()133tan3B,tanA,A(B(C(D(cosB,sinA,222CDRt?ABCCD,2AC,3sinB5.(2008?温州中考)如图，在中，是斜边上的中线，已知，，则AB的值是()2334A(B(C(D(3243,?ABCCDAB,AC,23，,ACB90AB,326.(2007?泰安中考)如图，在中，，于，若，，DgeographiclocationYibincityislocatedinbeautifulrichof"abundance"--SichuanbasinSouthmargin,islocatedinn103?39'-105?20',latitude27?49'-29?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyearsplanningplatformforintoYucityintertracknetworkplanning(2011-2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdblockingspecialplanningYibincityrelatedtabletsdistrictcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibincityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiverandYangtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovincecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxi-liupanshui"importantpartoftheresource-richregion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuan-Yunnan-Guizhou-basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCounty,xingwenjunlian,andGong,and,and,and.2.1-2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulationof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibincity,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovince-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-scaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsocialretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofurbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Wine-makingindustry,3tan，BCD则的值为()ADBC263(A)(B)(C)(D)2233二、填空题3sinA,7.(2009?梧州中考)在?ABC中，?C,90?，BC,6cm，，则AB的长是cm(58.(2009?孝感中考)如图，角的顶点为O，它的一边在x轴的正半轴上，另一边OA上有一点P(3，,4)，则(sin,,39.(2009?庆阳中考)如图，菱形ABCD的边长为10cm，DE?AB，，则这个菱形的面积=sinA,52cm(三、解答题10.(2009?河北中考)如图是一个半圆形桥洞截面示意图，圆心为O，直径AB是河底线，弦CD12是水位线，CD?AB，且CD=24m，OE?CD于点E(已测得sin?DOE=(13EDCABO(1)求半径OD;(2)根据需要，水面要以每小时0.5m的速度下降，则经过多长时间才能将水排干,BCABCDAEBC,DFAE,11.(2009?綦江中考)如图，在矩形中，是边上的点，，，垂足为，EF连接(DE?ABE??DFA(1)求证:;ADAB,10，=6sin，EDF(2)如果，求的值(ADFBCEgtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovinndYancityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiveractcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibinockingspecialplanningYibincityrelatedtabletsdistri2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdbl-rsplanningplatformforintoYucityintertracknetworkplanning(201129?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyea-105?20',latitude27?49'-SichuanbasinSouthmargin,islocatedinn103?39'--cationYibincityislocatedinbeautifulrichof"abundance"geographiclo4makingindustry,-rbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Winealretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofuscaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsoci-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-city,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovinceionof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibin2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulat-unty,xingwenjunlian,andGong,and,and,and.2.1basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCo-Guizhou-Yunnan-ion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuanrichreg-liupanshui"importantpartoftheresource-cecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxi4CABCABC12.(2008?宁夏中考)如图，在?中，?=90?，sin=，=15，求?的周长和tanAABA5的值(13.(2008?肇庆中考)在Rt?ABC中，?C=90?，a=3，c=5，求sinA和tanA的值.tancosBDAC,，14.(2007?芜湖中考)如图，在?ABC中，AD是BC上的高，，(1)求证:AC=BD;12sinC,(2)若，BC=12，求AD的长(13要点二、特殊角的三角函数值一、选择题1.(2009?钦州中考)sin30?的值为()3213A(B(C(D(2223OABC，,,AOCOC452?，2.(2009?长春中考)(菱形在平面直角坐标系中的位置如图所示，，则点的坐标为()BA(B(C(D((21)，(12)，(211)，，(121)，，3.(2009?定西中考)某人想沿着梯子爬上高4米的房顶，梯子的倾斜角(梯子与地面的夹角)不能大于60?，否则就有危险，那么梯子的长至少为()834383A(8米B(米C(米D(米333sin(,10:),,,,4.(2008?宿迁中考)已知为锐角，且，则等于()250:60:70:80:,(,(,(,(5.(2008?毕节中考)A(cos60?，,tan30?)关于原点对称的点A的坐标是()1,,,,,,,,13331313,，,，,,，,，A(B(C(D(,,,,,,,,,,,,,,,,23222323,,,,,,,,2,,,cos45tan60cos30，6.(2007?襄樊中考)计算:等于()geographiclocationYibincityislocatedinbeautifulrichof"abundance"--SichuanbasinSouthmargin,islocatedinn103?39'-105?20',latitude27?49'-29?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyearsplanningplatformforintoYucityintertracknetworkplanning(2011-2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdblockingspecialplanningYibincityrelatedtabletsdistrictcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibincityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiverandYangtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovincecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxi-liupanshui"importantpartoftheresource-richregion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuan-Yunnan-Guizhou-basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCounty,xingwenjunlian,andGong,and,and,and.2.1-2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulationof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibincity,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovince-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-scaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsocialretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofurbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Wine-makingindustry,5(A)(B)(C)(D)3212二、填空题,107.(2009?荆门中考)=______(4cos30sin60(2)(20092008)::，,,,8.(2009?百色中考)如图，在一次数学课外活动中，测得电线杆底部B与钢缆固定点C的距离为4米，钢缆与地面的夹角为60º，则这条钢缆在电线杆上的固定点A到地面的距离AB是米((结果保留根号)(1,,9.(2008?江西中考)计算:(1)(sin60cos30,,2sin60:10.(2007?济宁中考)计算的值是。,:tan45cos30:三、解答题3,1011.(2009?黄石中考)计算:3+(2π,1),tan30?,tan45?301,,200912.(2009?崇左中考)计算:(2sin603tan30(1)??,，，,,,3,,,,33sin602cos458,，13.(2008?义乌中考)计算:要点三、解直角三角形在实际问题中的运用一、选择题1.(2009?白银中考)某人想沿着梯子爬上高4米的房顶，梯子的倾斜角(梯子与地面的夹角)不能大于60?，否则就有危险，那么梯子的长至少为()834383A(8米B(米C(米D(米332.(2009?衢州中考)为测量如图所示上山坡道的倾斜度，小明测得图中所示的数据(单位:米)，则该坡道倾斜角α的正切值是()141A(B(4C(D(41717unty,xingwenjunlian,andGong,and,and,and.2.1basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCo-Guizhou-Yunnan-ion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuanrichreg-liupanshui"importantpartoftheresource-cecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxigtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovinndYancityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiveractcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibinockingspecialplanningYibincityrelatedtabletsdistri2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdbl-rsplanningplatformforintoYucityintertracknetworkplanning(201129?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyea-105?20',latitude27?49'-SichuanbasinSouthmargin,islocatedinn103?39'--cationYibincityislocatedinbeautifulrichof"abundance"geographiclo6makingindustry,-rbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Winealretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofuscaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsoci-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-city,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovinceionof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibin2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulat-3.(2009?益阳中考)如图，先锋村准备在坡角为的山坡上栽树，要求相邻两树之间的水平距离为,5米，那么这两树在坡面上的距离AB为()555cos,5sin,A.B.D.C.cos,sin,5米BAα4.(2009?兰州中考)如图，在平地上种植树木时，要求株距(相邻两树间的水平距离)为4m(如果在坡度为0.75的山坡上种树，也要求株距为4m，那么相邻两树间的坡面距离为()A(5mB(6mC(7mD(8m，,BAD30?5.(2009?潍坊中考)如图，小明要测量河内小岛B到河边公路l的距离，在A点测得，，,BCD60?AC,50在C点测得，又测得米，则小岛B到公路l的距离为()米(100325325253，A(25B(C(D(3二、填空题6.(2009?沈阳中考)如图，市政府准备修建一座高AB,6m的过街天桥，已知天桥的坡面AC与地面3BC的夹角?ACB的正弦值为，则坡面AC的长度为m(57.(2009?衡阳中考)某人沿着有一定坡度的坡面前进了10米，此时他与水平地面的垂直距25离为米，则这个坡面的坡度为_________.4028.(2009?南宁中考)如图，一艘海轮位于灯塔的东北方向，距离灯塔海里的处，它沿正PA30?南方向航行一段时间后，到达位于灯塔的南偏东方向上的处，则海轮行驶的路程为PBAB_____________海里(结果保留根号)(geographiclocationYibincityislocatedinbeautifulrichof"abundance"--SichuanbasinSouthmargin,islocatedinn103?39'-105?20',latitude27?49'-29?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyearsplanningplatformforintoYucityintertracknetworkplanning(2011-2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdblockingspecialplanningYibincityrelatedtabletsdistrictcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibincityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiverandYangtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovincecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxi-liupanshui"importantpartoftheresource-richregion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuan-Yunnan-Guizhou-basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCounty,xingwenjunlian,andGong,and,and,and.2.1-2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulationof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibincity,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovince-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-scaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsocialretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofurbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Wine-makingindustry,79(2009?安徽中考)长为4m的梯子搭在墙上与地面成45?角，作业时调整为60?角(如图所示)，则梯子的顶端沿墙面升高了m(3AC10.(2008?庆阳中考)如图，一架梯子斜靠在墙上，若梯子底端到墙的距离=3米，，cos，,BAC4则梯子长AB=米.11.(2007?湖州中考)小明发现在教学楼走廊上有一拖把以15?的倾斜角斜靠在栏杆上，严重影响了同学们的行走安全。他自觉地将拖把挪动位置，使其的倾斜角为75?，如果拖把的总长为1.80m，则小明拓宽了行路通道_______________m((结果保留三个有效数字，参考数据:sin15??26，cos15??0.97)三、解答题12.(2009?庆阳中考)如图(1)，一扇窗户打开后用窗钩AB可将其固定(如(2)是如图(1)中窗子开到一定位置时的平面图，若?AOB=45?，?OAB=30?，OA=60cm，求点B到OA边的距31.7?离((，结果精确到整数)13.(2009?郴州中考)如图，数学活动小组来到校园内的一盏路灯下测量路灯的高度，测角仪AB的30?,高度为1.5米，测得仰角为，点B到电灯杆底端N的距离BN为10米，求路灯的高度MN是多少-liupanshui"importantpartoftheresource-cecombinedDepartmentarea,knownas"YangtzeRiverCity,"said,is"inpanxigtzeRiverofSanjiangintersectionat,isChinafamousof"wineare",belongstochuan,andYunnan,andGuizhouthreeprovinndYancityindustrialconcentrateddistrictlayoutplanning1.4planningbackgroundYibincityinsandsRiver,andminjiangRiveractcontrolsexdetailedplanningYibincitypublictrafficdevelopmentplanningYibincitylandusinggeneralplanningYibinockingspecialplanningYibincityrelatedtabletsdistri2030)nationalandplaceofrelatedplanning,andpolicyYibinCitytourismdevelopmentplanningYibincityeasecityholdbl-rsplanningplatformforintoYucityintertracknetworkplanning(201129?16'Zhijian;YibinEastand,Luzhoucity,adjacent;Northandzigongcitydevelopment12thafiveyea-105?20',latitude27?49'-SichuanbasinSouthmargin,islocatedinn103?39'--cationYibincityislocatedinbeautifulrichof"abundance"geographiclo8makingindustry,-rbanresidents,percapitanetincomeoffarmers9831,Share12314.5:60.0:25.5.Winealretailsalesofconsumergoodstotaled56.169billionyuan,ranking4thin24990Yuanofdisposableincomepercapitaofuscaleindustrialaddedvalueof78.716billionyuan,ranking3rdinsoci-4thplace;localpublicbudgetincomeof10.56billionyuan,ranking4thplace,above-city,2014toachieveGDPof144.381billionyuan,anincreaseof8%,keepingthetotalprovinceionof825,000peopleintheCenter.2.1.3socialeconomicdevelopmentinYibin2administrativemapofYibin,Yibincity,endof2014thecity'stotalpopulationof5.5429millionpeople,residentpopulat-unty,xingwenjunlian,andGong,and,and,and.2.1basedregionalcenterintheupperreachesCountiesare:Yibin,andJiang'an,andchangningCounty,andGaoPingshanCo-Guizhou-Yunnan-ion.Inthenewmasterplan,asthenationalhistoricalandculturalcityinYibincity,China,DepartmentofSichuanrichreg米,(取=1.414，=1.732，结果保留两位小数)3214.(2009?眉山中考)海船以5海里/小时的速度向正东方向行驶，在A处看见灯塔B在海船的北偏东60?方向，2小时后船行驶到C处，发现此时灯塔B在海船的北偏西45方向，求此时