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 2
yards below the top of the pole and attached to the ground at a point that is 6
yards from the base of the pole. Find the total number of yards of cable that will be required.
Let's call the point where the cables attach to the flagpole point A, and the point where each cable attaches to the ground point B.
First, we need to find the length of each cable. We can do this using the Pythagorean theorem, since we have a right triangle formed by the flagpole, the attachment point on the flagpole, and the attachment point on the ground.
The height of the flagpole is 10 yards, and the attachment point on the flagpole is 2 yards below the top, so its height is 8 yards. The attachment point on the ground is 6 yards away from the base of the pole. So we have a right triangle with one leg of 8 yards and one leg of 6 yards. Using the Pythagorean theorem, we can find the length of the hypotenuse, which is the length of the cable:
c^2 = a^2 + b^2
c^2 = 8^2 + 6^2
c^2 = 100
c = 10
So each cable has a length of 10 yards.
To find the total length of cable required, we just need to add up the lengths of all three cables:
total length = 3 x length of one cable
total length = 3 x 10
total length = 30
So 30 yards of cable will be required to support the flagpole.
To find the total number of yards of cable required, we need to calculate the length of each cable and then add them together.
First, let's find the length of the first cable:
The distance from the top of the flagpole to the point where the first cable is attached is 2 yards.
The distance from the base of the flagpole to the point where the first cable is attached is 6 yards.
Using the Pythagorean theorem, we can calculate the length of the first cable:
Length of the first cable = √(2^2 + 6^2) = √(4 + 36) = √40 = 2√10 yards
Next, let's find the length of the second cable. Since all three cables are attached at the same point on the flagpole, the lengths of the second and third cables will be equal.
The distance from the top of the flagpole to the point where the second cable is attached is 2 yards.
The distance from the base of the flagpole to the point where the second cable is attached is also 6 yards.
Using the Pythagorean theorem, we can calculate the length of the second cable:
Length of the second cable = √(2^2 + 6^2) = √(4 + 36) = √40 = 2√10 yards
Finally, let's find the total length of the cables by adding the lengths of the three cables together.
Total length of cables = Length of the first cable + 2 * Length of the second cable
Total length of cables = 2√10 + 2 * 2√10 = 2√10 + 4√10 = 6√10 yards
Therefore, the total number of yards of cable required is 6√10 yards.