document.write( "Question 785381: how we find lentgh of the diagonal in a regular pentagon whose length of the side is 3units? \n" ); document.write( "

Algebra.Com's Answer #477512 by KMST(5328) $\"\"$ $\"About$

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The exterior angles of a regular polygon with $\"n\"$ sidees measure
\n" ); document.write( " $\"360%5Eo%2Fn\"$ or, in radians, $\"2pi%2Fn\"$ .
\n" ); document.write( "The interior angles, being supplementary measure
\n" ); document.write( " $\"180%5Eo-360%5Eo%2Fn=%28n%2A180%5Eo-360%5Eo%29%2Fn=%28n-2%29180%5Eo%2Fn\"$ or
\n" ); document.write( " $\"pi-2pi%2Fn=+%28n-2%29pi%2Fn\"$
\n" ); document.write( "The interior angles of a regular pentagon measure
\n" ); document.write( " $\"3%2A180%5Eo%2F5=108%5Eo\"$ or $\"3pi%2F5\"$
\n" ); document.write( "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
\n" ); document.write( " $\"%28180%5Eo-108%5Eo%29%2F2=72%5Eo%2F2=36%5Eo\"$ or $\"%281%2F2%29%2A%28pi-3pi%2F5%29=%281%2F2%29%2A%282pi%2F5%29=pi%2F5\"$ .
\n" ); document.write( "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
\n" ); document.write( " $\"3cos%2836%5Eo%29\"$ or $\"3cos%28pi%2F5%29\"$
\n" ); document.write( "The length of the diagonal would be twice that long, approx. 4.854 units. \n" ); document.write( "

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