A 10 foot utility pole has a cable attached to the top of it that is secured to the ground 7 feet away. How long is the cable? round to the nearest tenth.
Using the Pythagorean theorem, we can solve for the length of the cable:
c² = a² + b²
where c is the length of the cable, a is the height of the pole, and b is the distance from the base of the pole to where the cable is secured.
Plugging in the given values, we get:
c² = 10² + 7²
c² = 100 + 49
c² = 149
c ≈ 12.2
Therefore, the length of the cable is approximately 12.2 feet when rounded to the nearest tenth.
The pole, the ground and the cable form a right triangle, where the pole is the height and the distance between the pole and the cable attachment point on the ground is the base. We can use the Pythagorean theorem to find the length of the cable (which is the hypotenuse):
a^2 + b^2 = c^2
where a = 10 feet (height of the pole), b = 7 feet (distance between the pole and the cable attachment point on the ground), and c = length of the cable.
10^2 + 7^2 = c^2
100 + 49 = c^2
149 = c^2
c = √149 ≈ 12.2
The length of the cable is approximately 12.2 feet, rounded to the nearest tenth.