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)Responses500 ft.500 ft.22.4 ft.22.4 ft.300 ft.300 ft.17.3 ft.
To find the length of the cable, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the support cable is the hypotenuse, and the distance from the pole to the ground and the distance from the anchor point to the pole form the other two sides of the triangle.
Let's call the length of the cable "c" and the distance from the pole to the ground "a". According to the problem, a = 20 ft. The distance from the anchor point to the pole is "b", and b = 10 ft.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
To find c, we take the square root of both sides of the equation:
c ≈ √500
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer is 22.4 ft.