在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长

在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长
在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长
在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac
若tanA=1/4,b=根号17,a的长

在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长在三角形ABC中,角A ,B ,C的对边分别是a,b,c.a^2+c^2=b^2-(根号2)ac 若tanA=1/4,b=根号17,a的长
因为a^2+c^2=b^2-√2ac,所以a^2+c^2-b^2=-√2ac
cosB=（a²+c²-b²）/2ac= -√2/2 ,B是三角形的一个角,sinB＞0,所以sinB=√2/2
tanA=1/4 所以sinA/cosA =1/4 ,又因为sin²A+cos²A=1 ,解得sinA=√17/17
根据正弦定理得到 a=sinA×b÷sinB=√2.

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由a^2+c^2=b^2-(根号2)ac 得B=π/4，因为tanA=1/4，所以sinA=1/(√17），
再由正弦定理得a/sinA=(√17)/sinB,即a=√2