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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