SOLUTION: a terrible windstorm snapped a big pine tree which remained hinged at the crack while the tip of the tree touched the ground 48 feet away. Paul decided to find the true height of t

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Question 304499: a terrible windstorm snapped a big pine tree which remained hinged at the crack while the tip of the tree touched the ground 48 feet away. Paul decided to find the true height of thetree before it broke. he placed a 25 foot ladder 15 feet from the base of the tree and the ladder just reached the break. what is the height of tree before it broke?

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Answer by nerdybill(7384) (Show Source):
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a terrible windstorm snapped a big pine tree which remained hinged at the crack while the tip of the tree touched the ground 48 feet away. Paul decided to find the true height of thetree before it broke. he placed a 25 foot ladder 15 feet from the base of the tree and the ladder just reached the break. what is the height of tree before it broke?
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First, determine the height of the tree from the ground to the break.
Let x = height of the tree from the ground to the break
then applying Pythagorean theorem
x^2 + 15^2 = 25^2
x^2 + 225 = 625
x^2 = 400
x = sqrt(400)
x = 20 feet
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Second, determine the height of tree from the break to the top
Let y = height of tree from the break to the top
then applying Pythagorean theorem
20^2 + 48^2 = y^2
400 + 2304 = y^2
2704 = y^2
sqrt(2704) = y
52 feet = y
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Height of tree = x+y = 20+52 = 72 feet