document.write( "Question 1013770: A boy flying a kite has 100 feet of string out when the kite lodges in a tree. He reels in 20 feet of the string as he walks 25 feet closer to the tree. How high in the tree is his kite stuck? \n" ); document.write( "

Algebra.Com's Answer #630050 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A boy flying a kite has 100 feet of string out when the kite lodges in a tree. He reels in 20 feet of the string as he walks
\n" ); document.write( "25 feet closer to the tree. How high in the tree is his kite stuck?
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\n" ); document.write( "\n" ); document.write( "I asked GOOGLE with this:
\n" ); document.write( "\"A boy flying a kite has 100 feet of string out when the kite lodges in a tree\"\r
\n" ); document.write( "\n" ); document.write( "And GOOGLE point me into this link
\n" ); document.write( "A boy flying a kite has 100 feet of string out when the kite lodges in a tree
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document.write( "This is two right triangles \r\n" );
document.write( "let h be height of kite in tree and x \r\n" );
document.write( "be unknown distance of boy from tree after \r\n" );
document.write( "walking closer so x+25 = distance of boy from \r\n" );
document.write( "tree when kite is stuck \r\n" );
document.write( "Using pythagorean theorem \r\n" );
document.write( "h² + x² = 80² and h² + (x+25)² =100² \r\n" );
document.write( "now from first equation \r\n" );
document.write( "x² = 6400 - h² \r\n" );
document.write( "and from 2nd equation \r\n" );
document.write( "h² + x² + 50x + 625 = 10000 \r\n" );
document.write( "since h² + x² = 6400 we can write \r\n" );
document.write( "6400 +50x + 625 = 10000 \r\n" );
document.write( "so \r\n" );
document.write( "50x +7025= 10000 \r\n" );
document.write( "subtract 7025 from both sides \r\n" );
document.write( "50x = 2975 \r\n" );
document.write( "divide both sides by 50 to obtain \r\n" );
document.write( "x = 59.5 feet \r\n" );
document.write( "now to get h \r\n" );
document.write( "h² = 6400 - (59.5)² = 2859.75 \r\n" );
document.write( "thus h=√2859.75 =53.476 feet \r\n" );
document.write( "since the directions say round to the nearest foot \r\n" );
document.write( "h = 53 feet\r\n" );
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