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) (Show Source): You can put this solution on YOUR website!
The exterior angles of a regular polygon with sidees measure
or, in radians, .
The interior angles, being supplementary measure
or
The interior angles of a regular pentagon measure
or
Two sides of the pentagon and a diagonal form an isosceles triamgle with a vertex angle measuring or , and two base angles measuring
or .
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
or
The length of the diagonal would be twice that long, approx. 4.854 units.
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