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)
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem 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 other two sides.
In this case, the pole, the ground, and the cable form a right triangle, with the cable serving as the hypotenuse. Let's call the length of the pole "x" and the distance of the cable from the pole on the ground "y". We are given that x = 20 ft and y = 10 ft.
Using the Pythagorean theorem, we have:
x^2 + y^2 = cable length^2
Substituting the given values, we have:
20^2 + 10^2 = cable length^2
Simplifying,
400 + 100 = cable length^2
500 = cable length^2
To find the cable length, we take the square root of both sides:
√500 ≈ 22.4
Therefore, the length of the cable is approximately 22.4 feet.