1.已知三角形的三个内角A,B,C 所对的边分别为a,b,c且sin(π/4 +A)=7根号2/10 ,0<A<π/4(1)求tanA的值(2).若△ABC的面积S=24 b=8,求a的值2.在△ABC中,角ABC得对边分别为abc(1)若sin(A+π/6) = 2cosA,求A
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 19:01:45
![1.已知三角形的三个内角A,B,C 所对的边分别为a,b,c且sin(π/4 +A)=7根号2/10 ,0<A<π/4(1)求tanA的值(2).若△ABC的面积S=24 b=8,求a的值2.在△ABC中,角ABC得对边分别为abc(1)若sin(A+π/6) = 2cosA,求A](/uploads/image/z/8696875-67-5.jpg?t=1.%E5%B7%B2%E7%9F%A5%E4%B8%89%E8%A7%92%E5%BD%A2%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92A%2CB%2CC+%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%E4%B8%94sin%28%CF%80%2F4+%2BA%29%3D7%E6%A0%B9%E5%8F%B72%2F10+%2C0%EF%BC%9CA%EF%BC%9C%CF%80%2F4%EF%BC%881%EF%BC%89%E6%B1%82tanA%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89.%E8%8B%A5%E2%96%B3ABC%E7%9A%84%E9%9D%A2%E7%A7%AFS%3D24+b%3D8%2C%E6%B1%82a%E7%9A%84%E5%80%BC2.%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E8%A7%92ABC%E5%BE%97%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAabc%EF%BC%881%EF%BC%89%E8%8B%A5sin%EF%BC%88A%2B%CF%80%2F6%29+%3D+2cosA%2C%E6%B1%82A)
1.已知三角形的三个内角A,B,C 所对的边分别为a,b,c且sin(π/4 +A)=7根号2/10 ,0<A<π/4(1)求tanA的值(2).若△ABC的面积S=24 b=8,求a的值2.在△ABC中,角ABC得对边分别为abc(1)若sin(A+π/6) = 2cosA,求A
1.已知三角形的三个内角A,B,C 所对的边分别为a,b,c且sin(π/4 +A)=7根号2/10 ,0<A<π/4(1)求tanA的值(2).若△ABC的面积S=24 b=8,求a的值2.在△ABC中,角ABC得对边分别为abc(1)若sin(A+π/6) = 2cosA,求A的值(2)若cosA=1/3 b=3c 求sinC的值
1.已知三角形的三个内角A,B,C 所对的边分别为a,b,c且sin(π/4 +A)=7根号2/10 ,0<A<π/4(1)求tanA的值(2).若△ABC的面积S=24 b=8,求a的值2.在△ABC中,角ABC得对边分别为abc(1)若sin(A+π/6) = 2cosA,求A
(1) 0<A<pai/4==>pai/4<A+pai/4<π/2===>cos(A+π/4)=根号[1-sin^2(A+π/4)]=根号(1-98/100)
=根号2/10===>tan(A+π/4)=7根号2/10 /根号2/10=7 即 (1+tanA)/(1-tanA)=7===>tanA=3/4
(2) tanA=3/4===>sinA=3/5 ,cosA=4/5
S=bcsinA/2=8c*3/5*1/2=12c/5=24===>c=10
a^2=b^2+c^2-2bccosA=8^2+10^2-2*8*10*4/5=6^2===>a=6.
2.(1) sin(A+π/6)=sinAcosπ/6+cosAsinπ/6=根号3/2*sinA+cosA/2=2cosA===>3*sinA=3cosA===>
tanA=根号3===>A=π/3.
(2)cosA=1/3===>A为锐角===》sinA=根号(1-cos^2A)=2根号2/3
a^2=b^2+c^2-2bccosA=(3c)^2+c^2-2*3c*c*1/3=10c^2-2c^2=8c^2==>sin^2A=8sin^2C===>
8/3=8sin^2C===>sinC=根号(1/3)=根号3/3
若有疑问,请追问.如果满意,请采纳我的答案,!