Algebra.Com's Answer #694929 by ikleyn(52797)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "In an acute triangle ABC, the altitudes AD and CE are drawn.
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document.write( "Find the length of the line segment DE if AB = 15 cm, BC = 18 cm, and AD = 10 cm.
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document.write( "0. Make a sketch to follow my arguments.\r\n" );
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document.write( "1. The area of the triangle ABC is\r\n" );
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document.write( " S =  =  , \r\n" );
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document.write( " which gives you an equation \r\n" );
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document.write( " 15*|CE| = 18*10.\r\n" );
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document.write( " It implies |CE| =  = 12 cm.\r\n" );
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document.write( "2. Then from the right-angled triangle BCE |BE| =  =  =  .\r\n" );
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document.write( "3. From the right-angled triangle ABD |BD| =  =  =  = 9.\r\n" );
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document.write( "4. From the right-angled triangle ABD cos(B) =  =  =  .\r\n" );
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document.write( "5. Now, to answer the problem's question, apply the cosine law:\r\n" );
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document.write( "  =  \r\n" );
document.write( " =  =  =  =  .\r\n" );
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document.write( " Hense, |DE| =  = 10.78 (approximately).\r\n" );
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document.write( "Solved.\r
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