根据余弦定理
a^2 = b^2 + c^2 - 2bc *cosA
则
b^2+c^2-a^2 = 2bc*cosA
又三角形面积同时为
S = (1/2)*bc*sinA
所以
1/4√3(b^2+c^2-a^2) = 1/4√3 * 2bc*cosA = (1/2)*bc*sinA
1/√3 * cosA = sinA
tanA = 1/√3
A = 30 度