SOLUTION: 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

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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?
Answer by ikleyn(52786) About Me  (Show Source):
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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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I asked GOOGLE with this:
"A boy flying a kite has 100 feet of string out when the kite lodges in a tree"
And GOOGLE point me into this link
A boy flying a kite has 100 feet of string out when the kite lodges in a tree

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=√2859.75 =53.476 feet 
since the directions say round to the nearest foot 
h = 53 feet