SOLUTION: Imagine a pole stuck in the ground in such a way that it sticks up perpendicularly and 12 ft of it is showing. Then, all of a sudden the wind knocks the top off and the top touches

Question 476553: Imagine a pole stuck in the ground in such a way that it sticks up perpendicularly and 12 ft of it is showing. Then, all of a sudden the wind knocks the top off and the top touches 4ft from the base. The top is partial attached. How high is the break? i am having trouble setting this problem up
Found 2 solutions by robertb, lwsshak3:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x = hypotenuse of the right triangle formed.
Then the perpendicular side of the right triangle will measure 12 - x feet, while the horizontal side will be 4 feet.
Then by the Pythagorean theorem,

<==>
==> 160 = 24x
==> x = 20/3
==> the break is up 12 - x = 16/3 feet, or approximately 5.33 feet.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Imagine a pole stuck in the ground in such a way that it sticks up perpendicularly and 12 ft of it is showing. Then, all of a sudden the wind knocks the top off and the top touches 4ft from the base. The top is partial attached. How high is the break? i am having trouble setting this problem up.
**
Draw a right triangle with the horizontal leg=4 ft, and the vertical leg=x, and the hypotenuse=y. x is the remaining portion of the stick that is still standing, and the hypotenuse (y) is the piece that broke off, the top of which touches the ground 4 ft from the base.
..
x+y=12
y^2-4^2=x^2
y=12-x
(12-x)^2-16=x^2
144-24x+x^2-16=x^2
24x=144-16=128
x=128/24=16/3 ft
ans:
The break is 16/3 ft above the ground
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