高二師生合用解三角形講義

1、解三角形講義一.正弦定理：1.正弦定理：（其中r是三角形外接圓的半徑）2.變形： 角化邊 acdb 邊化角 如：abc中，則abc是等腰三角形或直角三角形 ，則abc是等腰三角形。3.三角形內(nèi)角平分線定理：如圖abc中，ad是的角平分線，則ab4.abc中，已知銳角a，邊b，則時(shí)，無(wú)解；或時(shí)，有一個(gè)解；時(shí)，有兩個(gè)解。如：已知,求(有一個(gè)解)已知,求(有兩個(gè)解)注意：由正弦定理求角時(shí)，注意解的個(gè)數(shù)。二.三角形面積1.2. ,其中是三角形內(nèi)切圓半徑.注:由面積公式求角時(shí)注意解的個(gè)數(shù)三.余弦定理1.余弦定理： 2.變形： acdb注意整體代入，如：3.三角形中線：abc中， d是bc的中點(diǎn)，則4.三

2、角形的形狀若時(shí),角是銳角若時(shí),角是直角若時(shí),角是鈍角如:銳角三角形的三邊為,求x的取值范圍; 鈍角三角形的三邊為,求x的取值范圍;5.應(yīng)用用余弦定理求角時(shí)只有一個(gè)解已知,求邊題型1：正、余弦定理1、在abc中，由已知條件解三角形，其中有兩解的是（）ab=20，a=45，c=80ba=30，c=28，b=60ca=14，b=16，a=45da=12，c=15，a=1202、3、已知求的邊長(zhǎng)以及外接圓的面積。4、在中，若其面積，則=_。5、邊長(zhǎng)為5，7，8的三角形的最大角與最小角的和是（ ） a b c d 6、在中，7.（1）在abc中，已知，求b及a；題型2：三角形面積1在中，求的值和的面積。

3、 2在銳角中，則的值等于 ，的取值范圍為 . 3在中，角所對(duì)的邊分別為，且滿足， （i）求的面積； （ii）若，求的值 4在中，內(nèi)角a、b、c的對(duì)邊長(zhǎng)分別為、，已知，且 求b 題型3：三角形中求值問(wèn)題1的三個(gè)內(nèi)角為，求當(dāng)a為何值時(shí)，取得最大值，并求出這個(gè)最大值。2在中，角所對(duì)的邊分別為，且滿足， （i）求的面積； （ii）若，求的值題型4：三角形中的三角恒等變換問(wèn)題1在abc中，a、b、c分別是a、b、c的對(duì)邊長(zhǎng)，已知a、b、c成等比數(shù)列，且a2c2=acbc，求a的大小及的值。2在abc中，已知a、b、c成等差數(shù)列，求的值。題型5：正、余弦定理判斷三角形形狀1在abc中，若2cosbsina

4、sinc，則abc的形狀一定是（ ）a.等腰直角三角形 b.直角三角形 c.等腰三角形d.等邊三角形2在abc中，若，請(qǐng)判斷三角形的形狀。3在abc中，面積且判定三角形形狀。4在abc中，判斷三角形形狀。待添加的隱藏文字內(nèi)容3綜合應(yīng)用1.在中，為銳角，角所對(duì)的邊分別為（i）求的值；（ii）若，求的值。 winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slate

5、r has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd

6、 hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 of

7、floads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands

8、-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its abo

9、ut how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate inves

10、tigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the we

11、ather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where o

12、ur day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can e

13、xpect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake agains

14、t the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been im

15、pressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unn

16、oticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis