An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth.(1 point)
Options
500 ft
300 ft
22.4 ft
17.3 ft
I don't think its 500 or 300. So it's either 22.4 or 17.3
To find the length of the cable, we can use the Pythagorean theorem. Let's represent the length of the cable as "c", the distance from the pole to the ground as "a", and the distance from the anchor point to the base of the pole as "b".
According to the given information, we have:
a = 20 ft
b = 10 ft
The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
So, we have:
c^2 = a^2 + b^2
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides, we get:
c = √500
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
Thanks that was correct
You're welcome! I'm glad I could help. If you have any more questions, feel free to ask.
To find the length of the cable, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the pole, the support cable, and the ground form a right triangle.
Let's assign variables to the different sides of the triangle:
- Length of the pole: x ft.
- Height above the ground where the cable is attached to the pole: 20 ft.
- Distance from the base of the pole to where the cable is anchored on the ground: 10 ft.
According to the Pythagorean theorem, we have the equation:
x^2 = (20 ft)^2 + (10 ft)^2
Now, let's solve the equation to find the value of x.
To find the length of the cable, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this scenario, the pole, the ground, and the support cable form a right triangle. The length of the support cable is the hypotenuse, the distance of the anchor point from the base of the pole is one side, and the height of the attachment point on the pole is the other side.
Using the Pythagorean theorem, we can determine the length of the support cable.
Let's denote the length of the support cable as 'c', the distance of the anchor point from the base of the pole as 'a', and the height of the attachment point on the pole as 'b'.
According to the problem,
a = 10 ft (distance of anchor point from base)
b = 20 ft (height of attachment point on the pole)
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
Now, to find c (the length of the cable), we can take the square root of both sides:
c = √500
c ≈ 22.4 ft (rounded to the nearest tenth)
Therefore, the length of the support cable is approximately 22.4 ft. Hence, the correct option is 22.4 ft.