Relationship between triangle and golden ratio

AI Thread Summary
The discussion centers on the relationship between a 72-72-36 triangle and the golden ratio, particularly in relation to pentagons. The triangle's angles suggest a connection to the golden ratio through the properties of a pentagon, as the angle 72 degrees corresponds to 360/5. Participants suggest using the sine rule to explore this relationship, noting that the ratio of the long sides to the short side can reveal the golden ratio. Specifically, it is mentioned that 2 sin(π/10) equals the golden ratio. Understanding these geometric relationships can clarify the connection between the triangle and the golden ratio.
todd098
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I am having trouble finding the relationship between a 72-72-36 triangle and the golden ratio. Could someone point me in the right direction or explain it? Thanks
 
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Since 72 = 360/5, that triangle should be related to a pentagon, and I think the sides and the diagonals from pentagons are related by the golden ratio. I'm talking from memory, though, but it should be easy to check.
 
todd098 said:
I am having trouble finding the relationship between a 72-72-36 triangle and the golden ratio. Could someone point me in the right direction or explain it? Thanks

Did you ever consider looking at the ratio of the long sides to the short side of that triangle. Use the sine rule and I'm sure you'll find it easy enough.
 
Notice that 2 sin(Pi/10) = golden ratio
 

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