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在三角形ABC中,角A,B,C所对的边长分别a,b,c,且满足sinC-sinBcosA=0(1)
求角B的值(2)若cosA/2=2√5/5,求a/b+c的值
人气:379 ℃ 时间:2020-06-13 15:19:22
解答
马上,码字中、、、ok(1)sinC=sin(180-A-B)=sin(A+B)=sinAcosB+cosAsinB.
sinC-sinBcosA= sinAcosB+cosAsinB -sinBcosA=sinAcosB=0,
因 0
(2)(cosA/2)^2 = (2√5/5)^2 =4/5
cosA=2(cosA/2)^2-1 = 2*4/5 -1= 3/5, sinA=√[1-(cosA)^2] =√[1-(3/5)^2] =4/5
sinC=cosA=3/5
a/(b+c) = sinA/(sinB+sinC)=4/5 / (1+3/5) = 1/2
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