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 10ft from the be the pole. How long is the cable? Round to the nearest tenth (1 point)
500 n
173 m
224 n
O 300 n
To find the length of the cable, we can use the Pythagorean theorem.
Let the length of the cable be 'c'. The distance from the pole to the ground is given as 20 ft, which will be one side of our right triangle. The distance from the ground anchor to the pole is given as 10 ft, which will be the other side of our right triangle.
Using the Pythagorean theorem, we have:
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
Rounding to the nearest tenth, the length of the cable is approximately 22.4 ft.
So, the correct answer is closest to 22.4 ft, which is not one of the given options.
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.
Let's label the sides of the triangle:
- The height of the pole (from the ground to the attachment point) will be one side.
- The distance from the attachment point to the base of the pole will be another side.
- The length of the cable will be the hypotenuse.
Using the Pythagorean Theorem equation:
h^2 + b^2 = c^2
Given that the height of the pole is 20 ft and the distance from the base to the attachment point is 10 ft:
20^2 + 10^2 = c^2
400 + 100 = c^2
500 = c^2
To find the length of the cable, we take the square root of both sides:
sqrt(500) ≈ 22.4
Rounded to the nearest tenth, the length of the cable is approximately 22.4 ft.
Therefore, the correct answer is "O 300 n" is incorrect.
To find the length of the support cable, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length 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-angled triangle. The height of the pole (20 ft) represents one side of the triangle, and the horizontal distance from the anchor point on the ground to the pole (10 ft) represents the other side. The length of the support cable is the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the support cable:
length of support cable = √(height^2 + distance^2)
= √(20^2 + 10^2)
= √(400 + 100)
= √500
≈ 22.4 ft (rounded to the nearest tenth)
Therefore, the length of the support cable is approximately 22.4 ft. However, none of the provided answer options is 22.4 ft.