There are two poles. One is 60 feet tall and the other is 8 feet tall. they are 60 feet apart. How much wire would you need to connect the two poles?
To calculate the total length of wire needed to connect the two poles, we need to consider the horizontal distance between the poles and the height of each pole.
First, let's visualize the scenario. Imagine a straight line connecting the tops of the two poles. This line represents the length of wire required to connect them.
The horizontal distance between the poles is given as 60 feet, so this forms the base of a right triangle. The height of the taller pole is 60 feet, and the height of the shorter pole is 8 feet. Hence, the vertical distance (or the height) between the two poles is 60 - 8 = 52 feet.
By applying the Pythagorean Theorem, we can calculate the length of the wire connecting the two poles.
According to the theorem:
(a^2) + (b^2) = (c^2),
where:
a and b are the two sides of the right triangle,
c is the hypotenuse (in this case, the length of the wire).
In this context, a = 52 feet (the difference in height between the poles), b = 60 feet (the horizontal distance between the poles), and c represents the length of wire we want to find.
Plugging the known values into the equation:
(52^2) + (60^2) = (c^2),
2704 + 3600 = c^2,
6304 = c^2.
To find the value of c, we take the square root of both sides:
√6304 = √c^2,
79.37 ≈ c.
So, you would need approximately 79.37 feet of wire to connect the two poles.