Golden triangle (mathematics)

A golden triangle, also called a sublime triangle, is an isosceles triangle in which the duplicated side is in the golden ratio φ {\displaystyle \varphi } to the base side: a b = φ = 1 + 5 2 ≈ 1.618 034. {\displaystyle {a \over b}=\varphi ={1+{\sqrt {5}} \over 2}\approx 1.618~034.} == Angles == The vertex angle is: θ = 2 arcsin ⁡ b 2 a = 2 arcsin ⁡ 1 2 φ = 2 arcsin ⁡ 5 − 1 4 = π 5 rad = 36 ∘ .