lengths of sides in golden ratio isosceles triangles The figure below shows three different isosceles triangles. every triangle is either 36-36-108 or 36-72-72. The base of the outermost triangle has length $\phi$. 

Find the lengths of both lines AT and MT.
Can someone please help me figure this out? What I'm thinking so far is that $1+\phi=\phi^2$ has roots which are the golden ratio.
I found this image online (on wikipedia) and i think it is the solution but i don't know how to solve it or actually get these values


If you apply this formula to your first picture 1 + ϕ = ϕ*ϕ
then the length of AT + ϕ = ϕ*ϕ
so, length of AT equals ϕ*ϕ - ϕ
