Question

三角形ABC中，若b=asinC,c=asinB 则三角形ABC形状是

答案是等腰直角

Answer 1

根据正弦定理 a/sinA = b/sin B = c/sin C
所以 b=asinC = csinA, c=asinB = bsinA
所以 sin A = b/c = c/b,所以 b^2 = c^2,即b = c

因为 c = bsinA = (a *sinC) *sinA所以 c/sinC = a sinA
有因为 c/sinC = a/sinA
所以 a/sinA = asinA
sin A * sin A = 1,sin A = 1,A = 90度
所以 是等腰直角