SOLUTION: Two vertical poles of lengths 9 feet and 12 feet stand 13 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of

Algebra ->  Pythagorean-theorem -> SOLUTION: Two vertical poles of lengths 9 feet and 12 feet stand 13 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of       Log On


   

Question 793656: Two vertical poles of lengths 9 feet and 12 feet stand 13 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. Where should this point be located to use 25 feet of cable?
The points should be located ___ feet from the smaller pole to used 25 feet of cable.
(Round to three decimal places as needed.)
Answer by mananth(16946) About Me  (Show Source):
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Two vertical poles of lengths 9 feet and 12 feet stand 13 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. Where should this point be located to use 25 feet of cable?

Let the length of cable from top of small pole to ground be x
Let the distance at which it is pegged be y
The height of pole = 9 m
so apply Pythagoras theorem
x^2= Y^2+9^2
x^2-y^2=81
(x+y)(x-y)=81......................(1)
The other side
length of cable tied = (25-x)
distance pegged from bigger pole = (13-y)
height of pole = 12m
so apply Pythagoras theorem
(25-x)^2=12^2+(13-y)^2
625-50x+x^2=144+169-26y+y^2
x^2-y^2=144+169-26y+50x-625
But x^2-y^2 = 81
144+169-26y+50x-625=81
-26y+50x= 393...................(2)
y+x=25...........................(3)
solve for x & y