△ABC中,ABC所对的边分别为a,b,c,已知a=3,cosA=√6/3,B=A+π/2,①求b的值②求△ABC的面积△ABC中,B=2A,a=1,b=√3,求c边△ABC的内角A,B,C的对边分别为a,b,c,已知b=2,B=π/6,c=π/4,求△ABC的面积
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/11 23:18:34
![△ABC中,ABC所对的边分别为a,b,c,已知a=3,cosA=√6/3,B=A+π/2,①求b的值②求△ABC的面积△ABC中,B=2A,a=1,b=√3,求c边△ABC的内角A,B,C的对边分别为a,b,c,已知b=2,B=π/6,c=π/4,求△ABC的面积](/uploads/image/z/7104211-43-1.jpg?t=%E2%96%B3ABC%E4%B8%AD%2CABC%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E5%B7%B2%E7%9F%A5a%3D3%2CcosA%3D%E2%88%9A6%2F3%2CB%3DA%2B%CF%80%2F2%2C%E2%91%A0%E6%B1%82b%E7%9A%84%E5%80%BC%E2%91%A1%E6%B1%82%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AF%E2%96%B3ABC%E4%B8%AD%2CB%3D2A%2Ca%3D1%2Cb%3D%E2%88%9A3%2C%E6%B1%82c%E8%BE%B9%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E5%B7%B2%E7%9F%A5b%3D2%2CB%3D%CF%80%2F6%2Cc%3D%CF%80%2F4%2C%E6%B1%82%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AF)
△ABC中,ABC所对的边分别为a,b,c,已知a=3,cosA=√6/3,B=A+π/2,①求b的值②求△ABC的面积△ABC中,B=2A,a=1,b=√3,求c边△ABC的内角A,B,C的对边分别为a,b,c,已知b=2,B=π/6,c=π/4,求△ABC的面积
△ABC中,ABC所对的边分别为a,b,c,已知a=3,cosA=√6/3,B=A+π/2,①求b的值②求△ABC的面积
△ABC中,B=2A,a=1,b=√3,求c边
△ABC的内角A,B,C的对边分别为a,b,c,已知b=2,B=π/6,c=π/4,求△ABC的面积
△ABC中,ABC所对的边分别为a,b,c,已知a=3,cosA=√6/3,B=A+π/2,①求b的值②求△ABC的面积△ABC中,B=2A,a=1,b=√3,求c边△ABC的内角A,B,C的对边分别为a,b,c,已知b=2,B=π/6,c=π/4,求△ABC的面积
sinA=√3/3,sinB=sin(A+π/2)=cosA=√6/3.根据正弦定理:a/sinA=b/sinB,3/(√3/3)=b/(√6/3).所以b=3√2.C=π-A-B=π-A-A-π/2=π/2-2A.sinC=sin(π/2-2A)=cos2A=2(cosA)^2-1=1/3
所以S=(1/2)*a*b*sinC=(1/2)*3*3√2*(1/3)=3√2/2
由正弦定理得a/sinA=b/sinB,1/sinA=√3/sin(2A)=√3/(2sinAcosA)
所以2cosA=√3,cosA=√3/2 .所以A=30度.所以B=60度,所以C=90度.所以c=√(a^2+b^2)=2
由正弦定理得:b/sinB=c/sinC,2/(1/2)=c/(√2/2) ,得c=2√2
A=π-B-C=7π/12.sinA=sin(7π/12)=sin(π/3+π/4)=(√6+√2)/4
所以S=(1/2)*b*c*sinA=(1/2)*2*2√2*(√6+√2)/4=√3+1,即三角形面积为√3+1.