返回

初中三年级数学

首页
  • 解答题
    如图,要在某县某的一个林场东西方向的两地之间修一条公路MN,已知C点周围200米范围内为原始森林保护区,在MN 上的点A处测得C在A的北偏东45°方向上,从A向东走600米到达B处,测得C在点B的北偏西60°方向上。
    (1)MN是否穿过原始森林保护区?为什么?(参考数据:≈1.732)
    (2)若修路工程顺利进行,要使修路工程比原计划提前5天完成,需将原定的工作效率提高25%,则原计划完成这项工程需要多少天?

    本题信息:2010年河北省模拟题数学解答题难度较难 来源:叶新丽
  • 本题答案
    查看答案
本试题 “如图,要在某县某的一个林场东西方向的两地之间修一条公路MN,已知C点周围200米范围内为原始森林保护区,在MN 上的点A处测得C在A的北偏东45°方向上,从A向东...” 主要考查您对

分式方程的应用

解直角三角形

等考点的理解。关于这些考点您可以点击下面的选项卡查看详细档案。
  • 分式方程的应用
  • 解直角三角形

列分式方程解应用题和列整式方程解应用题步骤基本相同,但必须注意,要检验求得的解是否为原方程的根,以及是否符合题意。
列分式方程解应用题的一般步骤是:
①找等量关系(审):理解题意,弄清具体情境中的已知量与未知量以及它们之间的基本关系;
②设:设未知数,用含x(或其他字母)表示某个未知数,由该未知数与其他数量的关系,写出表示相关量的式子;
③列:找出相等关系,列出分式方程;
④解:解这个分式方程;
⑤检验:双重检验,先检验是否为增根,再检验是否符合题意;
⑥答:写出答案。

例题
南宁到昆明西站的路程为828KM,一列普通列车和一列直达快车都从南宁开往昆明。直达快车的速度是普通快车速度的1.5倍,普通快车出发2H后,直达快车出发,结果比普通列车先到4H,求两次的速度.
设普通车速度是x千米每小时则直达车是1.5x
由题意得:
828/x-828/1.5x=6 ,
(828×1.5-828)/1.5x=6 ,
414/1.5=6x,
x=46, 1.5x=69
答:普通车速度是46千米每小时,直达车是69千米每小时。

无解的含义:
1.解为增根。
2.整式方程无解。(如:0x不等于0.)


用分式解应用题的常见题型:
(1)行程问题有路程、时间和速度三个量,其关系式是路程=速度×时间,一般式以时间为等量关系。
(2)工程问题有工作效率、工作时间和工作总量三个量,其关系式是工作总量=工作效率×工作时间。
(3)增长率问题,其等量关系式是原量×(1+增长率)=增长后的量,原量×(1+减少率)=减少后的量。


概念:
在直角三角形中,除直角外,一共有五个元素,即三条边和两个锐角,由直角三角形中除直角外的已知元素,求出所有未知元素的过程叫做解直角三角形。

解直角三角形的边角关系:
在Rt△ABC中,∠C=90°,∠A,∠B,∠C所对的边分别为a,b,c,
(1)三边之间的关系:(勾股定理);
(2)锐角之间的关系:∠A+∠B=90°;
(3)边角之间的关系:

解直角三角形的函数值:

锐角三角函数:
sinA=a/c,cosA=b/c,tanA=a/b,cotA=b/a
(1)互余角的三角函数值之间的关系:
若∠ A+∠ B=90°,那么sinA=cosB或sinB=cosA
(2)同角的三角函数值之间的关系:
①sin2A+cos2A=1
②tanA=sinA/cosA
③tanA=1/tanB
④a/sinA=b/sinB=c/sinC
(3)锐角三角函数随角度的变化规律:
锐角∠A的tan值和sin值随着角度的增大而增大,cos值随着角度的增大而减小。


解直角三角形的应用:
一般步骤是:
(1)将实际问题抽象为数学问题(画图,转化为直角三角形的问题);
(2)根据题目的条件,适当选择锐角三角函数等去解三角形;
(3)得到数学问题的答案;
(4)还原为实际问题的答案。

解直角三角形的函数值列举:
sin1=0.01745240643728351 sin2=0.03489949670250097 sin3=0.05233595624294383
sin4=0.0697564737441253 sin5=0.08715574274765816 sin6=0.10452846326765346
sin7=0.12186934340514747 sin8=0.13917310096006544 sin9=0.15643446504023087
sin10=0.17364817766693033 sin11=0.1908089953765448 sin12=0.20791169081775931
sin13=0.22495105434386497 sin14=0.24192189559966773 sin15=0.25881904510252074
sin16=0.27563735581699916 sin17=0.2923717047227367 sin18=0.3090169943749474
sin19=0.3255681544571567 sin20=0.3420201433256687 sin21=0.35836794954530027
sin22=0.374606593415912 sin23=0.3907311284892737 sin24=0.40673664307580015
sin25=0.42261826174069944 sin26=0.4383711467890774 sin27=0.45399049973954675
sin28=0.4694715627858908 sin29=0.48480962024633706 sin30=0.49999999999999994
sin31=0.5150380749100542 sin32=0.5299192642332049 sin33=0.544639035015027
sin34=0.5591929034707468 sin35=0.573576436351046 sin36=0.5877852522924731
sin37=0.6018150231520483 sin38=0.6156614753256583 sin39=0.6293203910498375
sin40=0.6427876096865392 sin41=0.6560590289905073 sin42=0.6691306063588582
sin43=0.6819983600624985 sin44=0.6946583704589972 sin45=0.7071067811865475
sin46=0.7193398003386511 sin47=0.7313537016191705 sin48=0.7431448254773941
sin49=0.7547095802227719 sin50=0.766044443118978 sin51=0.7771459614569708
sin52=0.7880107536067219 sin53=0.7986355100472928 sin54=0.8090169943749474
sin55=0.8191520442889918 sin56=0.8290375725550417 sin57=0.8386705679454239
sin58=0.848048096156426 sin59=0.8571673007021122 sin60=0.8660254037844386
sin61=0.8746197071393957 sin62=0.8829475928589269 sin63=0.8910065241883678
sin64=0.898794046299167 sin65=0.9063077870366499 sin66=0.9135454576426009
sin67=0.9205048534524404 sin68=0.9271838545667873 sin69=0.9335804264972017
sin70=0.9396926207859083 sin71=0.9455185755993167 sin72=0.9510565162951535
sin73=0.9563047559630354 sin74=0.9612616959383189 sin75=0.9659258262890683
sin76=0.9702957262759965 sin77=0.9743700647852352 sin78=0.9781476007338057
sin79=0.981627183447664 sin80=0.984807753012208 sin81=0.9876883405951378
sin82=0.9902680687415704 sin83=0.992546151641322 sin84=0.9945218953682733
sin85=0.9961946980917455 sin86=0.9975640502598242 sin87=0.9986295347545738
sin88=0.9993908270190958 sin89=0.9998476951563913
sin90=1

cos1=0.9998476951563913 cos2=0.9993908270190958 cos3=0.9986295347545738
cos4=0.9975640502598242 cos5=0.9961946980917455 cos6=0.9945218953682733
cos7=0.992546151641322 cos8=0.9902680687415704 cos9=0.9876883405951378
cos10=0.984807753012208 cos11=0.981627183447664 cos12=0.9781476007338057
cos13=0.9743700647852352 cos14=0.9702957262759965 cos15=0.9659258262890683
cos16=0.9612616959383189 cos17=0.9563047559630355 cos18=0.9510565162951535
cos19=0.9455185755993168 cos20=0.9396926207859084 cos21=0.9335804264972017
cos22=0.9271838545667874 cos23=0.9205048534524404 cos24=0.9135454576426009
cos25=0.9063077870366499 cos26=0.898794046299167 cos27=0.8910065241883679
cos28=0.882947592858927 cos29=0.8746197071393957 cos30=0.8660254037844387
cos31=0.8571673007021123 cos32=0.848048096156426 cos33=0.838670567945424
cos34=0.8290375725550417 cos35=0.8191520442889918 cos36=0.8090169943749474
cos37=0.7986355100472928 cos38=0.7880107536067219 cos39=0.7771459614569709
cos40=0.766044443118978 cos41=0.754709580222772 cos42=0.7431448254773942
cos43=0.7313537016191705 cos44=0.7193398003386512 cos45=0.7071067811865476
cos46=0.6946583704589974 cos47=0.6819983600624985 cos48=0.6691306063588582
cos49=0.6560590289905074 cos50=0.6427876096865394 cos51=0.6293203910498375
cos52=0.6156614753256583 cos53=0.6018150231520484 cos54=0.5877852522924731
cos55=0.5735764363510462 cos56=0.5591929034707468 cos57=0.5446390350150272
cos58=0.5299192642332049 cos59=0.5150380749100544 cos60=0.5000000000000001
cos61=0.4848096202463371 cos62=0.46947156278589086 cos63=0.4539904997395468
cos64=0.43837114678907746 cos65=0.42261826174069944 cos66=0.4067366430758004
cos67=0.3907311284892737 cos68=0.3746065934159122 cos69=0.35836794954530015
cos70=0.3420201433256688 cos71=0.32556815445715675 cos72=0.30901699437494745
cos73=0.29237170472273677 cos74=0.27563735581699916 cos75=0.25881904510252074
cos76=0.24192189559966767 cos77=0.22495105434386514 cos78=0.20791169081775923
cos79=0.19080899537654491 cos80=0.17364817766693041 cos81=0.15643446504023092
cos82=0.13917310096006546 cos83=0.12186934340514749 cos84=0.10452846326765346
cos85=0.08715574274765836 cos86=0.06975647374412523 cos87=0.052335956242943966
cos88=0.03489949670250108 cos89=0.0174524064372836
cos90=0

tan1=0.017455064928217585 tan2=0.03492076949174773 tan3=0.052407779283041196
tan4=0.06992681194351041 tan5=0.08748866352592401 tan6=0.10510423526567646
tan7=0.1227845609029046 tan8=0.14054083470239145 tan9=0.15838444032453627
tan10=0.17632698070846497 tan11=0.19438030913771848 tan12=0.2125565616700221
tan13=0.2308681911255631 tan14=0.24932800284318068 tan15=0.2679491924311227
tan16=0.2867453857588079 tan17=0.30573068145866033 tan18=0.3249196962329063
tan19=0.34432761328966527 tan20=0.36397023426620234 tan21=0.3838640350354158
tan22=0.4040262258351568 tan23=0.4244748162096047 tan24=0.4452286853085361
tan25=0.4663076581549986 tan26=0.4877325885658614 tan27=0.5095254494944288
tan28=0.5317094316614788 tan29=0.554309051452769 tan30=0.5773502691896257
tan31=0.6008606190275604 tan32=0.6248693519093275 tan33=0.6494075931975104
tan34=0.6745085168424265 tan35=0.7002075382097097 tan36=0.7265425280053609
tan37=0.7535540501027942 tan38=0.7812856265067174 tan39=0.8097840331950072
tan40=0.8390996311772799 tan41=0.8692867378162267 tan42=0.9004040442978399
tan43=0.9325150861376618 tan44=0.9656887748070739 tan45=0.9999999999999999
tan46=1.0355303137905693 tan47=1.0723687100246826 tan48=1.1106125148291927
tan49=1.1503684072210092 tan50=1.19175359259421 tan51=1.234897156535051
tan52=1.2799416321930785 tan53=1.3270448216204098 tan54=1.3763819204711733
tan55=1.4281480067421144 tan56=1.4825609685127403 tan57=1.5398649638145827
tan58=1.6003345290410506 tan59=1.6642794823505173 tan60=1.7320508075688767
tan61=1.8040477552714235 tan62=1.8807264653463318 tan63=1.9626105055051503
tan64=2.050303841579296 tan65=2.1445069205095586 tan66=2.246036773904215
tan67=2.355852365823753 tan68=2.4750868534162946 tan69=2.6050890646938023
tan70=2.7474774194546216 tan71=2.904210877675822 tan72=3.0776835371752526
tan73=3.2708526184841404 tan74=3.4874144438409087 tan75=3.7320508075688776
tan76=4.0107809335358455 tan77=4.331475874284153 tan78=4.704630109478456
tan79=5.144554015970307 tan80=5.671281819617707 tan81=6.313751514675041
tan82=7.115369722384207 tan83=8.144346427974593 tan84=9.514364454222587
tan85=11.43005230276132 tan86=14.300666256711942 tan87=19.08113668772816
tan88=28.636253282915515 tan89=57.289961630759144
tan90=(无限)


发现相似题
与“如图,要在某县某的一个林场东西方向的两地之间修一条公路MN...”考查相似的试题有: