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
17.3 ft.
17.3 ft.
500 ft.
500 ft.
300 ft.
300 ft.
22.4 ft.
To find the length of the cable, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the pole is 20 ft and the distance from the base to the anchor point is 10 ft. Let's call the length of the cable x.
We can set up the equation as follows:
x^2 = 20^2 + 10^2
Simplifying, we have:
x^2 = 400 + 100
x^2 = 500
Taking the square root of both sides, we get:
x = √500
Using a calculator, the approximate value of √500 is 22.4 ft.
Therefore, the length of the cable is approximately 22.4 ft.
To find the length of the cable, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse (length of the cable) is equal to the sum of the squares of the other two sides.
Given that the support cable is attached to the pole 20 ft. from the ground, and anchored on the ground 10 ft. from the base of the pole, we have a right-angled triangle.
Let's label the sides of the triangle:
- The height of the pole: x
- The distance from the base of the pole to the anchor point: 10 ft
- The distance from the anchor point to the point where the cable is attached to the pole: 20 ft
Using the Pythagorean theorem, we have:
x^2 = (10^2) + (20^2)
x^2 = 100 + 400
x^2 = 500
Taking the square root of both sides, we get:
x ≈ √500
x ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft (rounded to the nearest tenth).
To find the length of the cable, we can use the Pythagorean Theorem, which states that in a right triangle, the square 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 serves as one side of the triangle, and the support cable and the ground form the other two sides. Let's call the length of the cable 'a', the distance from the base of the pole to the ground 'b', and the distance from the attached point on the pole to the ground 'c'.
According to the given information, 'b' is 10 ft and 'c' is 20 ft.
Using the Pythagorean Theorem, we have:
a^2 = b^2 + c^2
a^2 = 10^2 + 20^2
a^2 = 100 + 400
a^2 = 500
Take the square root of both sides to solve for 'a':
a = √500
Now, we can calculate the length of the cable by finding the square root of 500:
a ≈ 22.4 ft
Hence, the length of the cable is approximately 22.4 ft.