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.
22.4 ft.
500 ft.
17.3 ft.
22.4 ft.
are you sure that is correct and explain how
I apologize for the mistake in my previous response. The correct answer is 22.4 ft.
To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the length of the cable be represented as "c", the height of the pole be represented as "a" (20 ft), and the distance from the base of the pole to where the cable is anchored on the ground be represented as "b" (10 ft).
Applying the Pythagorean theorem:
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:
c = √500
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.