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document.write( "Alan has no clue as to how to solve an advanced trig problem like this,\r\n" );
document.write( "so he tries to say yours is a foolish question.\r\n" );
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document.write( "Draw a right triangle ABC with angle A = 18°, opposite side = BC = x,\r\n" );
document.write( "and hypotenuse = 1. That makes sin(18°)=opposite/hypotenuse = x/1 = x.\r\n" );
document.write( "So we want to find x.\r\n" );
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\r\n" );
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document.write( "The angle C is 90°-18° = 72°, so we indicate that:\r\n" );
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\r\n" );
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document.write( "We draw an identical right triangle ABD underneath:\r\n" );
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document.write( "
\r\n" );
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document.write( "Next we draw CE to bisect the 72° angle C into\r\n" );
document.write( "two 36° angles.\r\n" );
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document.write( "Let's let DE = y\r\n" );
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document.write( "
\r\n" );
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document.write( "Now triangles CDE is similar to triangle ACD, because they\r\n" );
document.write( "each have a 36° angle and a 72° angle. Also they are both isosceles.\r\n" );
document.write( "Triangle ACE is also isosceles because it has a 36° angle at both A \r\n" );
document.write( "and C. So AE=CE=CD.\r\n" );
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document.write( "Since AC=1=AD, AE = 1-y. By similar triangles,\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
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document.write( "We take the + since the - sign gives a negative answer.\r\n" );
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document.write( "
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document.write( "
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
