SOLUTION: how we find lentgh of the diagonal in a regular pentagon whose length of the side is 3units?

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Question 785381: how we find lentgh of the diagonal in a regular pentagon whose length of the side is 3units?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The exterior angles of a regular polygon with n sidees measure
360%5Eo%2Fn or, in radians, 2pi%2Fn.
The interior angles, being supplementary measure
180%5Eo-360%5Eo%2Fn=%28n%2A180%5Eo-360%5Eo%29%2Fn=%28n-2%29180%5Eo%2Fn or
pi-2pi%2Fn=+%28n-2%29pi%2Fn
The interior angles of a regular pentagon measure
3%2A180%5Eo%2F5=108%5Eo or 3pi%2F5
Two sides of the pentagon and a diagonal form an isosceles triamgle with a vertex angle measuring 3%2A180%5Eo%2F5=108%5Eo or 3pi%2F5, and two base angles measuring
%28180%5Eo-108%5Eo%29%2F2=72%5Eo%2F2=36%5Eo or %281%2F2%29%2A%28pi-3pi%2F5%29=%281%2F2%29%2A%282pi%2F5%29=pi%2F5.
In the case of the problem the diagonal is the base and the legs are the sides of length 3 units, so half of the base would be
3cos%2836%5Eo%29 or 3cos%28pi%2F5%29
The length of the diagonal would be twice that long, approx. 4.854 units.