Question 948661: a wire is attached to the top of a pole. the wire is 1 ft longer than the pole, and the distance from the wire on the ground to the bottom of the pole is 1 ft less than the height of the pole. find the length of the wire and the height of the pole
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a wire is attached to the top of a pole.
the wire is 1 ft longer than the pole, and the distance from the wire on the ground to the bottom of the pole is 1 ft less than the height of the pole.
find the length of the wire and the height of the pole
:
Let p = height of the pole
then
(p+1) = the length of the wire
and
(p-1) = distance from the pole to the wire at the ground
:
The wire, pole and ground form a right triangle
Using pythag; a^2 + b^2 = c^2, where
a = p
b = (p-1)
c = (p+1), the wire
:
p^2 + (p-1)^2 = (p+1)^2
p^2 + p^2 - 2b + 1 = p^2 + 2b +1
Collect like terms on the left
p^2 + p^2 - p^2 - 2b -2b + 1 - 1 = 0
p^2 - 4p = 0
p(p - 4) = 0
p = 4 ft is the height of the pole
:
;
Check this 4^2 + 3^2 = 5^2
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