A flagpole has the 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 point that is 9 yards from the base of the pole, Find the total number of feet of cable that will be required
[Use The Pythagorean Theorem to solve this exercise]
the cables are attached at a height of 12 yards.
The other leg of the right triangle is 9 yards.
this is just a 3-4-5 triangle scaled up to 9-12-15.
So, there are three 15-yard cables.
convert that to feet and you're done.
Hey Steve, I'm also stuck on this problem too. I understand the part about the height being 12 yards since the three cables are attached 4 yards below the top. I can't figure out how you ended up with 15 yards. When you say that the other leg is 9 yards, are you talking about the base of the triangle or the Hypotenuse?
Never Mind... I Just figured it out. Thanks Steve for help!!! :D
To find the length of each cable required, 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 lengths of the other two sides.
In this case, we have a right triangle formed by the flagpole, one of the cables, and the ground. The vertical side of the triangle represents the height of the flagpole, which is 16 yards. The horizontal side represents the distance from the base of the flagpole to the point where the cable is attached to the ground, which is 9 yards. The length of the hypotenuse represents the length of the cable.
Using the Pythagorean theorem, we can find the length of the hypotenuse (cable) as follows:
Length of cable = √((Height of flagpole)^2 + (Distance from base to cable attachment point)^2)
= √((16 yards)^2 + (9 yards)^2)
= √(256 yards^2 + 81 yards^2)
= √(337 yards^2)
= 18.36 yards (rounded to two decimal places)
Since there are three cables required, the total length of cable required will be:
Total length of cable = 3 * Length of cable
= 3 * 18.36 yards
= 55.08 yards (rounded to two decimal places)
Finally, we need to convert the length from yards to feet. Since there are 3 feet in a yard, the total length of cable required in feet will be:
Total length of cable in feet = Total length of cable * 3 feet/yard
= 55.08 yards * 3 feet/yard
= 165.24 feet (rounded to two decimal places)
Therefore, the total number of feet of cable that will be required is approximately 165.24 feet.