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
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 side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the cable "c", the height of the pole "a", and the distance from the base of the pole to the anchor point "b".
In this case, a = 20 ft 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
Taking the square root of both sides, we have:
c ≈ √500
c ≈ 22.36
Rounding to the nearest tenth, the length of the cable is approximately 22.4 ft.