在锐角三角形ABC中,角A,B,C所对的边分别是a,b,c,已知a=根号7,b=3,根号7倍sin 在锐角三角形ABC中，角A，B，C所对的边分别为a，b，c，...
\u5728\u4e09\u89d2\u5f62abc\u4e2d.\u5df2\u77e5a=2\uff0cb=2\u6839\u53f72\uff0cC=15\u00b0\uff0c\u6c42\u89d2A\uff0cB\u548c\u8fb9c\u7684\u503cA=30\u00b0\uff0cB=135\u00b0\uff0cc=\u221a6-\u221a2\u3002
\u89e3\uff1a\u56e0\u4e3acos15\u00b0=cos(45\u00b0-30\u00b0)
=cos45cos30+sin45sin30=(\u221a6+\u221a2)/4
\u90a3\u4e48\u6839\u636e\u4f59\u5f26\u5b9a\u7406\u53ef\u5f97\uff0c
c²=a²+b²-2abcosC
=4+8-8\u221a2*(\u221a6+\u221a2)/4
=(\u221a6-\u221a2)²
\u6240\u4ee5c=\u221a6-\u221a2
\u90a3\u4e48\u6839\u636e\u6b63\u5f26\u5b9a\u7406\uff0ca/sinA=b/sinB=c/sinC\uff0c\u53ef\u5f97\uff0c
2/sinA=(\u221a6-\u221a2)/[(\u221a6-\u221a2)/4]=4\uff0c
\u5219sinA=1/2\uff0c
\u56e0\u4e3aa<b\uff0c\u90a3\u4e48A<B\uff0c\u6240\u4ee5A\u662f\u9510\u89d2\uff0c
\u5219A=30\u00b0\uff0c\u90a3\u4e48B=180-A-C=135\u00b0
\u5373A=30\u00b0\uff0cB=135\u00b0\uff0cc=\u221a6-\u221a2\u3002
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u6b63\u5f26\u5b9a\u7406\u6027\u8d28
\u5728\u4efb\u610f\u25b3ABC\u4e2d\uff0c\u89d2A\u3001B\u3001C\u6240\u5bf9\u7684\u8fb9\u957f\u5206\u522b\u4e3aa\u3001b\u3001c\uff0c
\u90a3\u4e48\u6709a/sinA=b/sinB=c/sinC\u3002
2\u3001\u4f59\u5f26\u5b9a\u7406\u6027\u8d28
\u5bf9\u4e8e\u4efb\u610f\u4e09\u89d2\u5f62\uff0c\u4efb\u4f55\u4e00\u8fb9\u7684\u5e73\u65b9\u7b49\u4e8e\u5176\u4ed6\u4e24\u8fb9\u5e73\u65b9\u7684\u548c\u51cf\u53bb\u8fd9\u4e24\u8fb9\u4e0e\u5b83\u4eec\u5939\u89d2\u7684\u4f59\u5f26\u7684\u79ef\u7684\u4e24\u500d\u3002
\u5373\u82e5\u4e09\u8fb9\u4e3aa\uff0cb\uff0cc \u4e09\u89d2\u4e3aA\u3001B\u3001C\uff0c\u90a3\u4e48
c²=a²+b²-2abcosC\u3001b²=a²+c²-2accosB\u3001a²=c²+b²-2cbcosA
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6b63\u5f26\u5b9a\u7406
3b=2asinB\uff0c3sinB=2sinAsinB\uff0csinA=3/2=1.5\uff0c\u9898\u76ee\u51fa\u9519\u4e86
绛旓細濡傚浘鎵绀猴紝閿愯涓夎褰BC涓紝鈭燗銆佲垹B鎵瀵圭殑杈归暱鍒嗗埆涓篴銆乥銆俛路sinB=鈭3路b銆傝繃鐐笴浣淐D鈯B浜庣偣D锛岀敱2a路sinB=鈭3路b锛屽緱sinB=鈭3路b/(2a)鈭靛湪Rt鈻矪DC涓紝sinB=CD/BC=CD/a锛鈭碈D/a=鈭3路b/(2a)锛屸埓CD=鈭3路b/2锛屸埓鍦≧t鈻矨CD涓紝sinA=CD/AD=(鈭3路b/2)/b=鈭3/2锛屸埓...
绛旓細鍥犱负涓夎褰BC鐨勯潰绉疭=鈭3/4锛坆^2+c^2-a^2锛夊張鐢辨寮﹀畾鐞嗭紝寰 S=1/2bcsinA 鎵浠 b^2+c^2-a^2=2/鈭3 bcsinA a^2=b^2+c^2-2 1/鈭3 bcsinA 鎵浠 cosA=1/鈭3 sinA 鍗 tanA=鈭3 鎵浠 A=60掳銆
绛旓細cosB=sinB tanB=1 B=45 2,b^2=a^2+c^2-2ac*cos45 10=18+c^2-6c c^2-6c+8=0 (c-2)(c-4)=0 c1=2,c2=4
绛旓細(a-c)(sinA+sinC)=(a-b)sinB.鏍规嵁姝ｅ鸡瀹氱悊 (a-c)(a+c)=(a-b)b a²-c²=ab-b²a²+b²-c²=ab 鈭碿osC=(a²+b²-c²)/(2ab)=ab/(2ab)=1/2 鈭礐涓洪攼瑙 鈭碈=蟺/3 鈭碆=蟺-A-C=2蟺/3-A 鈭B涓閿愯锛鍒2蟺/3-A<...
绛旓細瑙ｏ細鈭碘柍ABC鏄閿愯涓夎褰 鈭存湁锛1锛塁=蟺-(A+B)锛2锛塻inA+cosA>0 锛3锛夎嫢sinB=cosB锛屽垯B=蟺/4 鈭祍in(A-B)=cosC ==>sin(A-B)=cos[蟺-(A+B)]==>sin(A-B)=-cos(A+B)==>sinAcosB-cosAsinB=-cosAcosB+sinAsinB ==>sinAsinB+cosAsinB=sinAcosB+cosAcosB ==>sinB(sinA+cosA)...
绛旓細1銆丼=(1/2)bcsinA=2鈭2 2銆乻inA=2鈭2/3锛屼笖A鏄閿愯锛鍒檆osA=鈭(1锛峴in²A)=1/3锛屽啀鐢变綑寮﹀畾鐞嗭紝寰楋細a²=b²锛媍²锛2bccosA=13锛4=9锛屽垯a=3
绛旓細绛旓細涓夎褰BC涓紝鍚戦噺m=(sinA,cosA)锛屽悜閲弉=(cosC,sinC)鍚戦噺m.鍚戦噺n=鈭3/2 1锛夊悜閲忕偣绉=鍚戦噺m.鍚戦噺n=sinAcosC+cosAsinC=鈭3/2 鎵浠ワ細sin(A+C)=鈭3/2 鎵浠ワ細A+C=60掳鎴栬匒+C=120掳 鎵浠ワ細B=120掳鎴栬60掳 鍥犱负锛氫笁瑙掑舰鏄閿愯涓夎褰 鎵浠ワ細B=60掳 2锛塨=3锛孊=60掳锛孉+C=120...
绛旓細b/sinB=c/sinC 璇佹槑 浣淏C涓婄殑楂楢D 鍦ㄧ洿瑙涓夎褰ABD涓 AD=AB*sinB=c*sinB 鍦ㄧ洿瑙掍笁瑙掑舰ACD涓 AD=AC*sinC=b*sinC 鎵浠 c*sinB=b*sinC 鎵浠/sinB=c/sinC
绛旓細1.B<90 2.2B<90 3.B+2B+>90 寰楀嚭 30<B<45 a/b=sinA/sinB=sin2B/sinB=2sinBcosB/sinB=2cosB 鍥犱负 30<B<45 鎵浠 鈭2/2<cosB<鈭3/2 鍗 鈭2<2cosB<鈭3 鈭2<a/b<鈭3
绛旓細鐢辨寮﹀畾鐞嗭細a/sinA=b/sinB=c/sinC=2R锛圧涓涓夎褰澶栨帴鍦嗗崐寰勶級,寰梐=2RsinA,b=2RsinB,浠ｅ叆寮忓瓙寰 2锛2RsinA锛塻inB=(鏍瑰彿3)2RsinB 绾﹂」寰梥inA=(鏍瑰彿3)/2 鍥犱负A鏄閿愯,鎵浠鏄60掳
