Sara P.

asked • 09/14/22

Where should this point be located to use 27 feet of​ cable?

Two vertical poles of lengths 10 feet and 13 feet stand 14 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.

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Mark M. answered • 09/14/22

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Draw and label a diagram

x is the distance from the 10 foot pole to the point on the ground

14 - x is the distance from the 13 foot pole to the point on the ground


x2 + 102 = length squared of cable from 10 foot pole

(14 - x)2 + 132 = length squared of cable from 13 foot pole


x2 + 102 + (14 - x)2 + 132 = 272


Can you solve for x and answer?

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Don L.

tutor
If I solve the equation as given, it gives me an answer of approximately x = 20.5, which is greater than the 14 foot interval between the poles. If I solve the equation sqrt(x^2 + 10^2) + sqrt((14 - x)^2 + 13^2) = 27, I get solutions of approximately 4.9 and 7.3 as the distance of the point on the ground from the 10 foot pole. Using these two values will give the length of the lines from the top of each pole to the point on the ground.
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09/17/22

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