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.
22.4 ft.
22.4 ft.
17.3 ft.
17.3 ft.
500 ft.
To find the length of the cable, we can use the Pythagorean theorem. The length of the cable is the hypotenuse of a right triangle with the pole as one leg and the support cable as the other leg.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
where c is the length of the cable, a is the length of the pole, and b is the length of the support cable.
In this case, a = 20 ft and b = 10 ft.
So, c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides, we get:
c = sqrt(500) ≈ 22.4 ft
So, the length of the cable is approximately 22.4 ft.