A flagpole has a height of 10 yards. It will be supported by three cables, each of which is attached to the flagpole at a point 4 yards below the top and attached to the ground at a point that is 8 yards from the base of the pole. Find the total number of feet of cable that will be required
if you draw a diagram, you will quickly see that the cables form the hypotenuse of a 6-8-10 right triangle.
So, how much cable in 3 wires?
To find the total number of feet of cable required, we first need to calculate the length of each cable.
Let's consider one of the cables. It is attached to the flagpole 4 yards below the top, which means its vertical length is 10 yards - 4 yards = 6 yards.
The cable is also attached to the ground 8 yards from the base of the pole. We can consider this as the hypotenuse of a right triangle where one leg is the horizontal distance from the base to the attachment point on the ground and the other leg is the vertical length of the cable.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
⦁ Horizontal leg length = 8 yards
⦁ Vertical leg length = 6 yards
Hypotenuse length = sqrt((Horizontal leg length)^2 + (Vertical leg length)^2)
Hypotenuse length = sqrt((8 yards)^2 + (6 yards)^2)
Hypotenuse length = sqrt(64 yards^2 + 36 yards^2)
Hypotenuse length = sqrt(100 yards^2)
Hypotenuse length = 10 yards
Therefore, each cable requires 10 yards of length.
To find the total number of feet of cable required, we need to convert the yards to feet. Since 1 yard equals 3 feet, the total number of feet of cable required is:
Total number of feet of cable = 3 cables * 10 yards * 3 feet/yard
Total number of feet of cable = 90 feet
Therefore, the total number of feet of cable required to support the flagpole is 90 feet.