Question 1013770
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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?
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"A boy flying a kite has 100 feet of string out when the kite lodges in a tree"

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<A HREF=https://answers.yahoo.com/question/index?qid=20080730143712AAquX2x>A boy flying a kite has 100 feet of string out when the kite lodges in a tree</A>
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<pre>
This is two right triangles 
let h be height of kite in tree and x 
be unknown distance of boy from tree after 
walking closer so x+25 = distance of boy from 
tree when kite is stuck 
Using pythagorean theorem 
h² + x² = 80² and h² + (x+25)² =100² 
now from first equation 
x² = 6400 - h² 
and from 2nd equation 
h² + x² + 50x + 625 = 10000 
since h² + x² = 6400 we can write 
6400 +50x + 625 = 10000 
so 
50x +7025= 10000 
subtract 7025 from both sides 
50x = 2975 
divide both sides by 50 to obtain 
x = 59.5 feet 
now to get h 
h² = 6400 - (59.5)² = 2859.75 
thus h=&#8730;2859.75 =53.476 feet 
since the directions say round to the nearest foot 
h = 53 feet
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