I would like to find the apothem of a regular

OIPLZLqm6

OIPLZLqm6

Answered question

2022-02-28

I would like to find the apothem of a regular pentagon. It follows from
cos2π5=1+54
But how can this be proved (geometrically or trigonometrically)?

Answer & Explanation

cassidacc4

cassidacc4

Beginner2022-03-01Added 7 answers

Note that
22π5+32π5=2π,
therefore
cos(22π5)=cos(32π5)
Put cos2π5=x. Using the formulas
cos2x=2cos2x1, cos3x=4cos3x3cosx,
we have
4x32x23x+1=0(x1)(4x2+2x1)=0
Because cos2π51, we get
4x2+2x1=0
Another way, cos2π5>0, then cos2π5=1+54

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?