To find the length of the cable, we can use the Pythagorean theorem for a right-angled triangle. The triangle that is formed by the pole, the ground, and the cable is a right-angled triangle, where:
- The vertical pole represents one leg (20 ft),
- The horizontal distance from the pole to where the cable is anchored (10 ft) represents the other leg,
- The hypotenuse is the cable length that we want to find.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c² = a² + b²
Here, we are given:
a (height) = 20 ft
b (base) = 10 ft
We need to find c (cable length):
c² = a² + b²
c² = 20² + 10²
c² = 400 + 100
c² = 500
Now we take the square root of both sides to solve for c:
c = √500
To get an approximate value:
c ≈ √500
c ≈ 22.4
Therefore, the length of the cable is approximately 22.4 ft. The correct answer is:
22.4 ft.
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
22.4 ft.
22.4 ft.
17.3 ft.
17.3 ft.
300 ft.
300 ft.
500 ft.
1 answer