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 hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume that the length of the cable is represented by the variable "x".
According to the problem, the distance from the pole to the ground is 20 ft, and the distance from the base of the pole to the anchor point on the ground is 10 ft.
So, we can set up the following equation:
x² = 20² + 10²
x² = 400 + 100
x² = 500
Taking the square root of both sides of the equation, we find:
x ≈ √500 ≈ 22.4 ft
Rounded to the nearest tenth, 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, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assume the length of the cable is "c", the height of the pole is "a", and the distance between the pole and the anchor point is "b".
In this case, "a" is 20 ft and "b" is 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 get:
c = sqrt(500) ≈ 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, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the support cable forms a right triangle with the vertical pole and the cable's anchor point on the ground. The length of one side (the height of the pole) is given as 20 ft, and the length of the other side (the distance from the base of the pole to the anchor point on the ground) is given as 10 ft.
Let's denote the hypotenuse (the length of the support cable) as 'c', the height of the pole as 'a', and the distance from the base of the pole to the anchor point on the ground as 'b'.
According to the Pythagorean theorem, we have the equation:
c^2 = a^2 + b^2
Substituting the given values, we get:
c^2 = (20 ft)^2 + (10 ft)^2
c^2 = 400 ft^2 + 100 ft^2
c^2 = 500 ft^2
To find c, we take the square root of both sides of the equation:
c = √(500 ft^2)
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft (rounded to the nearest tenth).