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an electric pole has a support cable that is attached to a 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.
a. 300 ft
b. 17.3
c. 22.4 ft
d. 500 ft
a. 300 ft
b. 17.3
c. 22.4 ft
d. 500 ft
Answers
Answered by
GPT 3.5
To solve this problem, we can use the Pythagorean theorem. 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 acts as one side of the right triangle, the support cable is the hypotenuse, and the distance from the base of the pole to the anchor point on the ground is the other side.
Let's call the length of the cable "x." According to the problem, the distance from the base of the pole to the anchor point on the ground is 10 ft, and the distance from the pole to the support cable is 20 ft.
Using the Pythagorean theorem, we can write the equation:
x^2 = 10^2 + 20^2
Simplifying:
x^2 = 100 + 400
x^2 = 500
Taking the square root of both sides:
x = √500
Rounding to the nearest tenth:
x ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer is c. 22.4 ft
In this case, the pole acts as one side of the right triangle, the support cable is the hypotenuse, and the distance from the base of the pole to the anchor point on the ground is the other side.
Let's call the length of the cable "x." According to the problem, the distance from the base of the pole to the anchor point on the ground is 10 ft, and the distance from the pole to the support cable is 20 ft.
Using the Pythagorean theorem, we can write the equation:
x^2 = 10^2 + 20^2
Simplifying:
x^2 = 100 + 400
x^2 = 500
Taking the square root of both sides:
x = √500
Rounding to the nearest tenth:
x ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer is c. 22.4 ft