A flagpole has a height of 16 yards. It will be supported by three cables, each of which is attached to the flagpole at a point 4 yards below the top of the pole and attached to the ground at a point that is 9 yards from the base of the pole. Find the total number of feet of cable that will be required.
the length x of each cable is given by
x^2 = 9^2 + 12^2
Think 3-4-5 triangle and multiply by 3.
Ok. I got it. Thank you!
15
To find the total length of the three cables required to support the flagpole, we can use the Pythagorean theorem.
First, let's calculate the length of the hypotenuse of each cable (which represents the distance from the point where the cable is attached to the flagpole to the point where it is attached to the ground).
Using the Pythagorean theorem, the length of each hypotenuse is given by:
hypotenuse = √(base^2 + height^2)
For each cable:
base = 9 yards
height = 16 - 4 = 12 yards (since it is attached 4 yards below the top of the pole)
Using the formula, we can calculate the length of each hypotenuse:
hypotenuse = √(9^2 + 12^2)
= √(81 + 144)
= √225
= 15 yards
Therefore, the length of each cable is 15 yards.
Since there are three cables in total, we can multiply the length of one cable by 3 to find the total length of the cables required:
Total length of cables = 15 yards * 3
= 45 yards
To convert this length to feet, we know that 1 yard is equivalent to 3 feet. Therefore, we can multiply the total length of cables by 3 to convert it to feet:
Total length of cables = 45 yards * 3 feet/yard
= 135 feet
Therefore, the total number of feet of cable required to support the flagpole is 135 feet.