Golden triangle (mathematics)

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A golden triangle is an isosceles triangle in which the two longer sides have equal lengths and in which the ratio of this length to that of the third, smaller side is the golden ratio

\varphi = {1 + \sqrt{5} \over 2}.

This is the shape of the triangles found in the points of pentagrams.

The vertex angle is equal to

 \theta = \cos^{-1}\left( {\varphi \over 2}\right) = {\pi \over 5} = 36^\circ.

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