A 12 foot pole is supported by a wire that extends from the top of the pole to a point that is 16 feet from the base of the pole. Use the Pythagorean Theorem to find the length of the wire
Using the Pythagorean Theorem, we have:
Length of wire^2 = Length of pole^2 + Distance from pole to base^2
Length of wire^2 = 12^2 + 16^2
Length of wire^2 = 144 + 256
Length of wire^2 = 400
Taking the square root of both sides, we have:
Length of wire = sqrt(400)
Length of wire = 20 feet
To find the length of the wire, we can use the Pythagorean Theorem, which states that in a right 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 other two sides.
In this case, we have a right triangle formed by the pole, the wire, and the ground. The pole is the vertical side, the horizontal side is the distance from the base of the pole to the point where the wire is supported, and the wire itself is the hypotenuse.
The length of the pole, which is the vertical side, is given as 12 feet.
The distance from the base of the pole to the point where the wire is supported, which is the horizontal side, is given as 16 feet.
Using the Pythagorean Theorem, we can calculate the length of the wire as follows:
Length of wire = sqrt(Length of pole^2 + Distance^2)
Substituting in the given values:
Length of wire = sqrt(12^2 + 16^2)
Length of wire = sqrt(144 + 256)
Length of wire = sqrt(400)
Length of wire = 20 feet
Therefore, the length of the wire is 20 feet.