高二师生合用解三角形讲义

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1、解三角形讲义一.正弦定理：1.正弦定理：（其中R是三角形外接圆的半径）2.变形： 角化边 ACDB 边化角 如：ABC中，则ABC是等腰三角形或直角三角形 ，则ABC是等腰三角形。3.三角形内角平分线定理：如图ABC中，AD是的角平分线，则Ab4.ABC中，已知锐角A，边b，则时，无解；或时，有一个解；时，有两个解。如：已知,求(有一个解)已知,求(有两个解)注意：由正弦定理求角时，注意解的个数。二.三角形面积1.2. ,其中是三角形内切圆半径.注:由面积公式求角时注意解的个数三.余弦定理1.余弦定理： 2.变形： ACDB注意整体代入，如：3.三角形中线：ABC中， D是BC的中点，则4.三

2、角形的形状若时,角是锐角若时,角是直角若时,角是钝角如:锐角三角形的三边为,求x的取值范围; 钝角三角形的三边为,求x的取值范围;5.应用用余弦定理求角时只有一个解已知,求边题型1：正、余弦定理1、在ABC中，由已知条件解三角形，其中有两解的是（）Ab=20，A=45，C=80Ba=30，c=28，B=60Ca=14，b=16，A=45Da=12，c=15，A=1202、3、已知求的边长以及外接圆的面积。4、在中，若其面积，则=_。5、边长为5，7，8的三角形的最大角与最小角的和是（ ） A B C D 6、在中，7.（1）在ABC中，已知，求b及A；题型2：三角形面积1在中，求的值和的面积。

3、 2在锐角中，则的值等于 ，的取值范围为 . 3在中，角所对的边分别为，且满足， （I）求的面积； （II）若，求的值 4在中，内角A、B、C的对边长分别为、，已知，且 求b 题型3：三角形中求值问题1的三个内角为，求当A为何值时，取得最大值，并求出这个最大值。2在中，角所对的边分别为，且满足， （I）求的面积； （II）若，求的值题型4：三角形中的三角恒等变换问题1在ABC中，a、b、c分别是A、B、C的对边长，已知a、b、c成等比数列，且a2c2=acbc，求A的大小及的值。2在ABC中，已知A、B、C成等差数列，求的值。题型5：正、余弦定理判断三角形形状1在ABC中，若2cosBsinA

4、sinC，则ABC的形状一定是（ ）A.等腰直角三角形 B.直角三角形 C.等腰三角形D.等边三角形2在ABC中，若，请判断三角形的形状。3在ABC中，面积且判定三角形形状。4在ABC中，判断三角形形状。待添加的隐藏文字内容3综合应用1.在中，为锐角，角所对的边分别为（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 s

17、o many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.