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Length of Wire connecting two poles of different height.

An electrician must attach ground wires to the tops of two poles that are 48 feet apart. One pole is 32 feet tall, and the other pole is 18 feet tall. The electrician decides to use a single wire to connect the tops of the two poles and anchor the wire to the ground halfway between the two poles. How much wire will he use?

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Quang H. | Math and Science TutorMath and Science Tutor
4.0 4.0 (2 lesson ratings) (2)
The general equation for the hypotenuse of a right triangle is:
a2 + b2 = c2
where a and b are the legs and c is the hypotenuse. We know the height of the two poles, and the line that connects the 2 tops of the poles is the hypotenuse. One leg of the triangle is 48 ft, the distance between the two poles, and the other leg is the height difference between the poles, which is 32 - 18 = 14 ft. Using the Pythagorean Theorem, we find that the hypotenuse is 50 feet.
I don't know what you mean by "anchor the wire to the ground halfway between the two poles", so I cannot answer the rest of the question. Sorry.
Phillip R. | Top Notch Math and Science Tutoring from Brown Univ GradTop Notch Math and Science Tutoring from...
The anchor wire cuts the connecting wire in half so the hypotenuse of a new triangle is 25 ft with horizontal leg = 24 ft. The vertical leg is therefore √ (625 - 576) = 7 ft. Add 7 ft to the length of the shorter pole 18 ft and we get 25 feet. Total wire length is 50 + 25 = 75 ft