SOLUTION: At a certain time of day, a tree that is x feet tall casts a shadow that is x-17 meters long. If the distance from the top of the tree to the end of the shadow is x+8 meters, what

Question 757456: At a certain time of day, a tree that is x feet tall casts a shadow that is x-17 meters long. If the distance from the top of the tree to the end of the shadow is x+8 meters, what is the height,x, of the tree?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
A Pythagoras question.
Tree = x
Shadow = x - 17
Distance from top of tree
to end of shadow = x + 8
So x^2 + (x - 17)^2 = (x + 8)^2
x^2 +(x^2 - 34x + 289) = (x^2 + 16x + 64)
Combine and collect like terms.
x^2 - 50x + 225
(x - 5)(x - 45)
So either x = 5 or x = 45
As the shadow = (x - 17) I would
discount x = 5.
Tree height = 45ft
Tree's shadow = 28ft
Distance from top of
tree to tip of shadow.
= 53ft.
Hope this helps.
:-)
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