document.write( "Question 207273This question is from textbook Longman Mathematics for IGCSE book 1
\n" ); document.write( ": A regular pentagon has sides of 10cm.
\n" ); document.write( "Find the radius the largest circle which can be drawn inside the pentagon.
\n" ); document.write( " Actually this question is from the chapter of Triginometry: Tangent ratios\r
\n" ); document.write( "\n" ); document.write( "Please tell me that how could I use tangent in this particular question.\r
\n" ); document.write( "\n" ); document.write( "I request you to solve my question as soon as possible. I would be highly glad. Thankyou very much indeed. \n" ); document.write( "

Algebra.Com's Answer #156734 by Edwin McCravy(20060) $\"\"$ $\"About$

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A regular pentagon has sides of 10cm.
\n" ); document.write( "Find the radius the largest circle which can be drawn inside the pentagon.
\n" ); document.write( "Actually this question is from the chapter of Triginometry: Tangent ratios
\n" ); document.write( "Please tell me that how could I use tangent in this particular question.
\n" ); document.write( "I request you to solve my question as soon as possible. I would be highly glad. Thankyou very much indeed.
\n" ); document.write( "

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document.write( "Start with a regular pentagon all sides 10.\r\n" );
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document.write( "And we want the radius of this circle,\r\n" );
document.write( "which is tangent to all five sides:\r\n" );
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document.write( "Draw in all the \"spokes\", which will\r\n" );
document.write( "all be radii of the circle:\r\n" );
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document.write( "The angle marked is  because \r\n" );
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document.write( "Next we erase the three upper spokes and concentrate\r\n" );
document.write( "only on the bottom triangle:\r\n" );
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document.write( "Draw the alititude to the base, which\r\n" );
document.write( "bisects the 72° angle into two 36°\r\n" );
document.write( "angles, and which also bisects the base\r\n" );
document.write( "into two segments, each 5cm.  The desired\r\n" );
document.write( "circle will be tangent to the base at\r\n" );
document.write( "the midpoint, and the radius of the\r\n" );
document.write( "circle will be this altitude, marked\r\n" );
document.write( "as r.\r\n" );
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document.write( "Observing only the right triangle\r\n" );
document.write( "on the left,\r\n" );
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document.write( "the side opposite the 36° angle is\r\n" );
document.write( "5, and r is the side adjacent to\r\n" );
document.write( "the 36° angle, so we use tangent:\r\n" );
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document.write( "Multiply both sides by r:\r\n" );
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document.write( "Divide both sides by \r\n" );
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document.write( "Edwin

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