SOLUTION: Lightning hit a tree three-eighths of the distance up the trunk from the ground and broke the tree so that its top landed 40 feet from the base of the trunk as shown. How tall was

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Question 378118: Lightning hit a tree three-eighths of the distance up the trunk from the ground and broke the tree so that its top landed 40 feet from the base of the trunk as shown. How tall was the tree originally? Show all work.
Answer by mananth(16946) (Show Source):
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let height of tree be x feet
lightening struck 3x/8 up the tree and broke
Balance 5x/8 fell such that top was 40 feet from base.
5x/8 = hypotenuse
one leg = 40
other leg = 3x/8
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apply Pythagoras theorem
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(5x/8)^2= 40^2+(3x/8)^2
25x^2/64 = 1600 +9x^2/64
-9x^2/64
25x^2/64 -9x^2/64 = 1600
(25x^2-9x^2)/64 =1600
multiply by 64
16x^2=64*1600
/16
x^2=64*1600/16
x^2=4*1600
take the square root
x= sqrt(4*1600)
x=2*40
x=80 feet the height of the tree.
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m.ananth@hotmail.ca