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.
300 ft.
300 ft.
22.4 ft.
22.4 ft.
500 ft.
To find the length of the cable, we can use the Pythagorean theorem. The length of the cable is the hypotenuse of a right triangle, with the support cable as one side and the distance from the base of the pole to the anchor point as the other side.
Using the Pythagorean theorem, the length of the cable can be found:
c^2 = a^2 + b^2
where c is the length of the cable, a is the length of the support cable (20 ft), and b is the distance from the base of the pole to the anchor point (10 ft).
Plugging in the values:
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking 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, you can use the Pythagorean theorem, which states that in a right-angled 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 pole, the support cable, and the ground form a right-angled triangle. The pole is the vertical side, the support cable is the hypotenuse, and the ground is the horizontal side.
The vertical side (pole) is 20 ft. and the horizontal side (ground) is 10 ft.
To find the length of the hypotenuse (support cable), you can use the Pythagorean theorem:
Support cable squared = vertical side squared + horizontal side squared
Support cable squared = 20 ft. squared + 10 ft. squared
Support cable squared = 400 ft. + 100 ft.
Support cable squared = 500 ft.
Taking the square root of both sides, we can find the length of the support cable:
Support cable = sqrt(500) ft.
Support cable ≈ 22.4 ft. (rounded to the nearest tenth)
Therefore, the correct answer is 22.4 ft.