Final answer:
The length of the electrical wire needed to stretch from the top of a 10-foot power pole to a transformer 4 feet away is found using the Pythagorean theorem. It turns out to be approximately 10.77 feet long.
Step-by-step explanation:
The question is asking for the length of the electrical wire needed to stretch from the top of a 10-foot power pole to a transformer that is 4 feet from the base of the pole. This scenario forms a right-angled triangle, where the power pole is the vertical side, the distance from the pole to the transformer is the horizontal side, and the wire is the hypotenuse. To find the length of the electrical wire, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Calculation using Pythagorean theorem:
Length of power pole (vertical side): 10 feet
Distance from base of pole to transformer (horizontal side): 4 feet
Length of electrical wire (hypotenuse): Unknown
Using the Pythagorean theorem: Hypotenuse2 = Vertical side2 + Horizontal side2
Wire length2 = 102 + 42 = 100 + 16 = 116
Wire length = √116 ≈ 10.77 feet
The electrical wire must be approximately 10.77 feet long to stretch from the top of the pole to the transformer.