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 find the length of the cable. Let's call the length of the cable "c" and the distance from the base of the pole to the attachment point on the ground "a". According to the problem, we have a = 10 ft and the height of the pole "b" is 20 ft.
Using the Pythagorean theorem: c² = a² + b²
c² = 10² + 20²
c² = 100 + 400
c² = 500
Taking the square root of both sides to solve for c:
c = √500
c ≈ 22.4
Therefore, the length of the cable is approximately 22.4 ft.
To find the length of the cable, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the pole acts as the vertical side, the distance from the base of the pole to the anchor point acts as the horizontal side, and the cable acts as the hypotenuse.
Let's define the sides:
- The length of the pole (vertical side) is 20 ft.
- The distance from the base of the pole to the anchor point (horizontal side) is 10 ft.
Using the Pythagorean theorem, we can find the length of the cable (hypotenuse):
c² = a² + b²
where c is the length of the cable, and a and b are the lengths of the other two sides.
Plugging in the values:
c² = 20² + 10²
c² = 400 + 100
c² = 500
To solve for c, we take the square root of both sides:
c = √500
c ≈ 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, which states that 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 cable forms the hypotenuse of a right triangle.
Let's denote the length of the cable as "c", the distance from the pole to the ground as "a", and the distance from the anchor point to the base of the pole as "b".
According to the information given, a = 20 ft and b = 10 ft.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Substituting the known values, we get:
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
To find c, we take the square root of both sides:
c = sqrt(500)
Using a calculator, we can find that sqrt(500) ≈ 22.4.
Therefore, the length of the cable is approximately 22.4 ft (rounded to the nearest tenth).