document.write( "Question 557966: What is the length of the shortest altitude of a triangle with the sides of 13, 14, and 15? \n" ); document.write( "

Algebra.Com's Answer #362993 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The other tutor's answer is correct, but maybe you're studying the \r\n" );
document.write( "law of cosines instead of Heron's formula.  And maybe you haven't\r\n" );
document.write( "proved that the shortest altitude is the one to the longest side.\r\n" );
document.write( "(His \"inverse proportional\" statement is incorrect).\r\n" );
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document.write( "Maybe this is the approach you should take.\r\n" );
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document.write( "Let's draw the three altitudes:\r\n" );
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document.write( "The law of cosines for the cos(A) is\r\n" );
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document.write( " =  =  =  =  \r\n" );
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document.write( " =  =  =  =  =  =  = \r\n" );
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document.write( " = \r\n" );
document.write( " = \r\n" );
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document.write( "Multiply both sides by 13:\r\n" );
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document.write( "The law of cosines for cos(B)\r\n" );
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document.write( " =  =  =  = \r\n" );
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document.write( " =  =  =  =  =  =  = \r\n" );
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document.write( " = \r\n" );
document.write( " = \r\n" );
document.write( "Cross multiply\r\n" );
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document.write( " =  which we have already calculated as \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
document.write( "Cross multiply\r\n" );
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document.write( "So  is the shortest altitude.\r\n" );
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document.write( "Incidentally, if you draw all three altitudes, they all three\r\n" );
document.write( "intersect at the same point, called the orthocenter.\r\n" );
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document.write( "Edwin

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