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)
Responses
300 ft.
300 ft.
500 ft.
500 ft.
22.4 ft.
22.4 ft.
17.3 ft.
The cable forms a right triangle with the ground and the pole. The vertical side of the triangle represents the height of the pole, which is 20 ft. The horizontal side represents the distance from the base of the pole to the anchor point on the ground, which is 10 ft.
Using the Pythagorean theorem, we can find the length of the cable:
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 find:
c = √500
c ≈ 22.4 ft.
Therefore, the length of the cable is approximately 22.4 ft.
To find the length of the cable, we can use the Pythagorean theorem. According to the given information, the pole, support cable, and the ground form a right triangle.
Let the length of the cable be "c." The distance from the base of the pole to the point where the cable is attached is 10 ft and the distance from the ground to the point where the cable is attached is 20 ft.
Using the Pythagorean theorem, we have:
c² = (10²) + (20²)
c² = 100 + 400
c² = 500
Taking the square root of both sides, we get:
c ≈ √500
c ≈ 22.4
Therefore, the length of the cable is approximately 22.4 ft. So, the correct answer is:
22.4 ft.
To find the length of the cable, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with one side of length 20 ft (height above the ground) and another side of length 10 ft (distance from the base of the pole to the cable anchor point).
Let's label the unknown length of the cable as "a". Using the Pythagorean theorem, we have:
a^2 = (20 ft)^2 + (10 ft)^2
a^2 = 400 ft^2 + 100 ft^2
a^2 = 500 ft^2
Taking the square root of both sides, we find:
a ≈ √500 ft
a ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
So the correct answer is 22.4 ft.