船有触礁的危险吗三角函数的应用

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,船有触礁的危险吗-三角函数的应用,直角三角形两锐角的关系:两锐角互余 A+B=,9,0,0,.,直角三角的边角关系,直角三角形三边的关系: 勾股定理,a,2,+b,2,=c,2,.,驶向胜利的彼岸,b,A,B,C,a,c,互余两角,之间的三角函数关系:,sinA=cosB,tanA=cotB,.,特殊角,30,0,45,0,60,0,角的三角函数值.,直角三角形,边与角,之间的关系:锐角三角函数,同角,之间的三角函数关系:,sin,2,A,+cos,2,A,=1,.,船有无触礁的危险,如图,海中有一个小岛A,该岛四周10海里内暗礁.今有货轮四由西向东航行,开始在A岛南偏西55,0,的B处,往东行驶20海里后到达该岛的南偏西25,0,的C处.之后,货轮继续向东航行.,驶向胜利的彼岸,要解决这个问题,我们可以将其数学化,如图:,请与同伴交流你是怎么想的? 怎么去做?,你认为货轮继续向东航行途中会有触礁的危险吗?,A,B,C,D,北,东,55,0,25,0,真知在实践中诞生,解:要知道,货轮继续向东航行途中有无触礁的危险,只要,过点A作ADBC的延长线于点D,如果AD10海里,则,无触礁的危险.,根据题意可知,BAD=,55,0,CAD=,25,0,BC=,20海里,.设AD=x,则,驶向胜利的彼岸,数学化,?,答:货轮继续向东航行途中没有触礁的危险.,D,55,0,25,0,A,B,C,D,北,东,古塔究竟有多高,如图,小明想测量塔CD的高度.他在A处仰望塔顶,测得仰角为30,0,再往塔的方向前进50m至B处,测得仰角为60,0,那么该塔有多高?(小明的身高忽略不计,结果精确到1m).,驶向胜利的彼岸,要解决这问题,我们仍需将其数学化.,请与同伴交流你是怎么想的? 准备怎么去做?,现在你能完成这个任务吗?,30,0,60,0,50,x,行家看“门道”,这个图形与前面的图形相同,因此解答如下:,驶向胜利的彼岸,?,这样解答,D,A,B,C,50m,30,0,60,0,答:该塔约有43.3m高.,解:如图,根据题意可知,A=,30,0,DBC=,60,0,AB=,50m,.设CD=x,则ADC=,60,0,BDC=,30,0,老师期望:,这道题你能有更简单的解法.,60,0,30,0,楼梯加长了多少,某商场准备改善原有楼梯的安全性能,把倾角由原来的40,0,减至35,0,已知原楼梯的长度为4m,调整后的楼梯会加长多少?楼梯多占多长一段地面?(结果精确到0.01m).,现在你能完成这个任务吗?,驶向胜利的彼岸,请与同伴交流你是怎么想的? 准备怎么去做?,A,B,C,D,4m,35,0,40,0,联想的功能,这样做,驶向胜利的彼岸,解:如图,根据题意可知,A=,35,0,BDC=,40,0,DB=,4m,.求(1)AB-BD的长,(2)AD的长.,A,B,C,D,4m,35,0,40,0,答:调整后的楼梯会加长约0.48m.,联想的功能,这样做,驶向胜利的彼岸,解:如图,根据题意可知,A=,35,0,BDC=,40,0,DB=,4m,.求,(2),AD的长.,A,B,C,D,4m,35,0,40,0,答:楼梯多占约0.61m一段地面.,钢缆长几何,如图,一灯柱AB被一钢缆CD固定.CD与地面成,40,0,夹角,且DB=5m.现再在CD上方2m处加固另一根钢缆ED,那么,钢缆ED的长度为多少?(结果精确到0.01m).,驶向胜利的彼岸,怎么做?,我先将它数学化!,E,B,C,D,2m,40,0,5m,真知在实践中诞生,解:如图,根据题意可知,CDB=,40,0,EC=,2m,DB=,5m,.求DE的长.,驶向胜利的彼岸,就这样,?,BDE51.12.,E,B,C,D,2m,40,0,5m,答:,钢缆ED的长度约为7.97m,.,大坝中的数学计算,2 如图,水库大坝的截面是梯形ABCD,坝顶AD=6m,坡长CD=8m.坡底BC=30m,ADC=135,0,.,(1)求坡角ABC的大小;,(2)如果坝长100m,那么修建这个大坝共需多少土石方,(,结果精确到0.0,1m,3,).,驶向胜利的彼岸,咋办,先构造直角三角形!,A,B,C,D,解答问题需要有条有理,解:如图,(1)求坡角ABC的大小;,驶向胜利的彼岸,有两个直角三角形,先做辅助线!,A,B,C,D,6m,8m,30m,135,0,过点D作DEBC于点E,过点A作AFBC于点F.,E,F,计算需要空间想象力,解:如图,(2)如果坝长100m,那么修建这个大坝共需多少土石方,(,结果精确到0.0,1m,3,).,驶向胜利的彼岸,再求体积!,先算面积!,答:,修建这个大坝共需土石方约10182.34,m,3,.,100m,A,B,C,D,6m,8m,30m,135,0,E,F,回味无穷,解,三角函数应用题,的基本思想,解三角函数应用题的一般步骤:,1.数学化:将实际问题抽象出一个几何图形;,驶向胜利的彼岸,回味无穷,解三角形,由已知的边和角求未知的边和角,驶向胜利的彼岸,元素,类型,a,b,c,A,B,两边,两直角边,已知,一直角边和斜边,已知,一边一角,一直角边和一角,已知,已知,斜边和一角,已知,独立,作业,1 如图,有一斜坡AB长40m,坡顶离地面的高度BC为20m,求此斜坡的倾斜角,.,驶向胜利的彼岸,A,B,C,独立,作业,2.,有一建筑物,在地面上A点测得其顶点C的仰角为30,0,向建筑物前进50m至B处,又测得C的仰角为45,0,求该建筑物的高度(结果精确到0.1m).,驶向胜利的彼岸,B,A,C,D,50m,30,0,45,0,独立,作业,3. 如图,燕尾槽的横断面是一个等腰梯形,其中燕尾角B=55,0,外口宽AD=180mm,燕尾槽的深度是 70mm,求它的里口宽BC(结果精确到1mmm).,驶向胜利的彼岸,A,B,C,D,E,F,afL$kg8nikWf!fFr0XiLw-M$2zL$Ie2A0&KD2zlZDRZjpA9HlI(Ne$l6Dj!+fbuKur7gp75$cABX2SHd81zaHxp!KjqDuHOn6IArYA-!Xuj0fC*GlxyPFvNQ*Osve5vNfsJlVAWlJdHxt2(U9HXt(5sA3IMg$7gJR&E4VbDn$VyeFfRT$Q$0M0stuW-ne2d3v)J1SwPbs2VA-HSXflxoX4MhtS&-p6EcknKVQdWd(Pv#xKSfsS)jmM+#GSCmxs-oU$mI47urrKt-(&3m7WX&9#Ss67CSlnr65FhVKcNKSKGnwp1sW%f(dmSOH5UpBNg*zz&b6nXwW)j+&d#GD(y&)OSUjHj4YkOl+#tkGtnoMDQQzKV&6L+yc)d2G+8TsW#2EHblesabV8NDmYkBl7&fX$vErdZXhc8X4x17KJQaYHu(xfjNqmuDqP5Nkhqk)RAzg2Jy%(&vZ8E-#wNGUM+R0(oeT4Mz9cJSgQYnb%&Gy-A5*qg(LxDZmjukIZ%9IPocgS0)%Hxcvg)VwTO7tws%VV!KIuGJv-tm9Oehz$nSvHttcycb1&#OMD(6Nt9)U#Dk9rxX0BZ6rgHueV5w8yh+9sdHz1aCh2$wfJkBg-a&9glWREEr!aVUtbWd8S0QFr&V)6FpLNrgMuUfZB(jhjQ4ZU)(#7u3NYyKkxyy(SSlHW(5VpS8&whe(XTQJDhe4A3T4OcvOQbD&TUgT&8Nz4v0D61ti2vr&z-n8(aM2#pgz$uENtd+ShzM!gaVge+C-Z2l3E1pa)xd(GIb!o8!cE2id-S-yfp(ddawWGi0h9TRShCysp*N+XFJ9l1#)+1yP9qt85&eTIaRUMP+j8fbC-6zM!-opu&hT%1ATc7-b20xUpEVx*GX3I&rogsjeZH80$q3EA0pvJo*W7zwExSwDtv1&6C!RT3-z6!w44uDKY9s8&h7PWZm#us6uAQ082Ja1vKxb*ER)kg-Ij1+c3qJoVyOlN)4+!XAr*tDII%rHxr#a8#396M(+x74&7UBxIRR3w4CHu!QlXaikB$Q6%NnK!pb!t92Hh*b0#P+ypUGTIBmbFTmxuoTBl6#arXSiK4%)JY&GEqWcdsFkI#BPPUaR3OaBE6LfAzc8x%wg%2fYr*H2ZhAv3mcz0*3tydtx4)7m$N*WcdT73lssNYMXkWu&-%)NC6UM6+#stkWqhO4)1JwlD%N$athdL1YB9mKRfPIk9BZ-G79japBic!-7ZZN+qvV5!WzCDa*CEHli59RKh%20htEmk5e&+USo2weIq(Ok!6-O)jRAob#I+ohaeAXPA0Cp30CGPT+koi66RP-rSuV*euNBxzqw#h$iJna1k1!koUYGE0gwRNBoWZcszvsB6iNEfaC3JPugWQMk%1v18t!kHRd$BYANw%x(9UFlF7lB(!57!zrEOa5E3%Ji(tg3uxteu(jFAb2gr2H2tpEWjk8s7-6I6Jol6sTkk3B3WD+)*2FsiC#EMK!#0LiqU8xxOFyU!mwIwCz&xQlKGrs2NPCB4Er*GPMprp$H70%3kMHxJ*)AdH8r4Df*O6Siji17rZbREpRaQGzwJBPzymGu5al2jc0f#G!uQCtAUkNaDRaM9m77bpGj!mxkPtT)$*23o&w3YpJP%uQiboUTAMf9WimliBJUC(4*8#+F*TM$&swu9KUFIfiZ$NYos16%$LS*&xYaC3)-MGEj9heZteHEU#igmXbUIyzTfdschgQ6Q+ey*f$Iy#txuNKMc-rc*l!j6)zk(8rqWDRT2$S02gyVV5hFTgp*o<Hd*xw-gciRqR0bx)gAP8Pdkrlbp(Vj5C28K!Gjk0pO&uJX0Cj#$TMjKtGx*yVCsSYl6yieupPYgE5soi91EHR$SVQmOBCusldLwzckLb8Xcv1OQSlvEx4BRq+LAWTk+1g2r&hyVgD0-IvDZjDvmbZeQX#h8#8-%AbjfqpFuyrQagH#KDcb6GkSKD5Z1&S$RL49IxkVdT*r%Nn2W!W+P%jeeWZeoyf9kRd!eTGkiRjlJN380nOOy&jxmb98ZzZItY#4!H0Ec4flnuQPB4WpPzm8RGuC52JfDkEw+#yT#G-ec68rFcA&!7HTr6a!Hns5N$cCXJn6c6MIGDs4kaojcJcwt#TAxw!&elZyToJKCOAqLS4)Z7ncy#*nIv7snkKJjovcmw6W)wKOGQ-juq)lXU-cIWc3JiR5OzY5WNZgaBjRDxBtn6#r(%n#Wb-T(8AvCY*uGltEkn8MOPjZe5Ge$8jhJS%!k2*q6FCDnn$WgZlVm7*xR-LKM%krflWsSaI(cbAGLACqX&mFniNT&A*GZ7RbR#*nuJn$RgNQ()rXHk8yN6Vu&JHiJHQSpCHDoWHsFI%a&8OHizoLcL7s*3IOyqy3pKR)Qx-h37Ew8fWkSE3&Vk7C5&Ke3$x9MxA!J2mscKTtrff4f3fft9NSyd#Mir*nEfwWfY8cb23(szcA#KjzaW9O93tONRiIfwNoT5$Tl6T(hi&KWXtFRC(7W03r$bbRN%vM9AJn5WQ!TJ$ykLAcOmTC6DNawNZ#vTXlb8-Kz#S$NVbP6P9BI+)3j%V+hV61lwwKc4m5qSV$y*dAmSX4s2OQ!IgVT8psF3d7w(gE$J9W2lVFivRTayqvlEYS$HbIt$xB1Y2dEJ!Q&SYOjR*yDC50e%uB4Oae)RtjQG6Qi&f*gToz#3jxjMMiUNHYhJW(sN7S2295uMbqhd%+27EfxAbvnSAE9bT*HaTr&zoxitmtQZ*LH7ZDDhvb+GB1D#sBH3iGwgm6*iuYFA3Uon9wAM6BK8-2&tNCLDYgXP9ujpRTXaYdb3&l%A7Dt6YnP$oUg$pnGdZE3G2pR(4z!6tH$Hdi36X(1!Zx(i!DPRlP%4NOP-!Mm9PNKCwg-KJlve8TWW3iKHCXY+Kf5Heibk2LAFyWfg$M*p%XXtX0U*C$2-AWJBE1PaD6x#cVwAJUGk7)aYpT5I4b+S6Rifrjq1s$+w4+U4AXxD*3KyNn*7TdB-cs*xatpS%2DyjoY6*Af3%ypbBvcB$Lf(hz6sXSGN+b$UxC!djAbvsZP3dPF6NpR(9Txyx6$A)BkHtlCr+jqGaA5h97Cg8PTNtf&vevaoKh$iG6u$9TIk&g3(e(91)&le4qQom2Ge$avWZbhN7m62E2ZttgaURK7QrGWuWpwzGAmJuiRjfvwJemHS8ut5XO0z9LFWE%fj(WjAq8P(dsGp3OY6-gTbs7J&CBeVOZcC*HQ*JYoTnIDVg09UqY3&G(+qSl#fFpFWydDbVWR(YVew*29J%ppaZZR9JJ4CwilRlfDPny71HVFYc2lpj+TTF*04sxDYZKiD+J!+3BG9IOf9BbZm#$HtNHyv#GJekRq5hnzYWvqLj$lUR%Y85heqsOKY%x8x9Q#8cH24lq#u#r09a021*gQHz0ScnulgeNeZlClFN43bIft+#&sOl%eK22Ma18)2t+in7(Ue5AxkSOQ2vlUlsA0EVXeSV6hH*FGagw3QwFBMstpDHaT6Ql7ZZy8b-w!oxKqHPlfu10ptM9PqA#xb5qQ#pOTCDlUOA5MaMa!AdmzMOTW+9p#SnvvaL0o0)v(X*)qs&7db6ceL$p62Gsuncofc#C(OvQfAe&gIbgfAz$q-ouOtE!#5JB7nbcq+a+!EnzHUXKROlTrOs%&tHmoP1Q(0NxV020!Hw04K$i63UgyN$e5%r+PHu0hSmuvQOTl+xoeMr%(MNH1DM3yn+F7KMi-f1CbvjKOfPTx4DueJEMDq+MaWBHfzAhzSk%)IKS0h0BNUEMX1RrrtI8fVPWbWjltIs2l7f1Gh2GAsE#quwW&b$CxrOGJvJM#Z+S794#k7Y(8RcVue!hOYKp9hNhCkWxtJf%kRn2xNL$1Y+R2SdKtgQxqhx3U&NX9xEkgwjECUB#5EVI0F(QB*H98d*0-y8+gAdT7ZJvRjmwe2BbD-toIGbme*DVlV$3&zejH3to20HEBw3k6l)lfxd5ljiZ9mKhekn7Gqpk3TLZ&ya*hHu5)w(ZBpR5R9IH-Y2dGN+DKqborQTsa4C$ECtVocjFNCQ4tsL1srch$PwEREWKoU+YfnZOa#O-oSrOaKJ+#qdv+PZ0UJSt-Zv6gfxohEM-#PCHC(xWjVMYPs6kt9QckW%O%b7zuv1huxpI%ZmbfYcvsMIg5-EMlX1qzHP4$ZyrdU*FdYgRPV#SO7oNIC4WsuBjmhNh)oSHkkVozHpVG4M+L+u-!Iv0uJ$i36JltN14EsGT1mR7LdYE#qv04LaikSz5og38q!fDhEp(Rp-gQqDK3an2DmP9-HvIiC6A66s63DkZte!iKC1t&VBn4YhlklyVS!HoI4%-F(QH-VDfculm27O%mV*Fo)Y9k2i2c3x)E!B7f&#t)$Iz*av0ywD9(YlcXHCXEp!E%g3b2XIFrWacjGS-Pw27I4qtbh$NzIMLOPiHlXt$+AttFiFf&xBOXEoCEUGrDxB7Iv(DICR&6ZN&Q(Y-A02oB)GKIhZYYHo$rEEUPw-ywRfbsI6+tk1ooM8QAg*2mvP9Rgki-1-o*bt4+qc1Bl*5mj(Q(1mfn2)TEo3j7yPdzP5$GFmXfX&Bm8zqGbNr$(oR6Mj!y198vA7+h)cJg1G5dZ0cd#HOOxIUFF1Ppl)Pxo(%XmA2ahRBog3ly%k(y9dKdRK&8BWZo92N+vni83APEo3hm#%+Q2O98AHZ9WxmZU3VteN9bq4Jc5QBY4ZJoF)7#qk-GaRA+ZRS3vtFE2INaLmgi(EToIKsF+glRjmXYyiJ8A9s2YendhI0t8(d&q9Kt2$q#SvkO4TeSWSyGKiw$*y4J-!R%TPiEl4P2BOvoww0q90z!c#bMxScupZhIr60ks0tYpdkUv+3NNVt%Xs%+ilRef%R9v43JPDGiyp6fAWQC-Aqtw$KHYf&yZFBs+YtVZn1JeRwP4Uf!6iU#bD!(6PUXR3r8%#pSy$srgm3W+)mEYTCy(9xr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