The golden triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of either of its equal
sides
to its base
is equal to the golden ratio, . From the above figure, this means that the triangle has vertex angle
equal to
(1)
or , and that the height is related to the base through
The triangles at the tips of a pentagram (left figure) and obtained by dividing a decagon by connecting
opposite vertices (right figure) are golden triangles.
This follows from the fact that
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to its base 
is equal to the golden ratio, 
. From the above figure, this means that the triangle has vertex angle
equal to
, and that the height 
is related to the base 
through
of a decagon
of side length 
is
, where 
is the golden ratio.
