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.
500 ft.
500 ft.
22.4 ft.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the length of the cable) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the cable "c", and the lengths of the two sides "a" and "b". We have:
a = 20 ft.
b = 10 ft.
Using the Pythagorean theorem, we can write:
c² = a² + b²
c² = (20 ft.)² + (10 ft.)²
c² = 400 ft² + 100 ft²
c² = 500 ft²
Taking the square root of both sides, we get:
c = √(500 ft²)
c ≈ 22.4 ft.
Therefore, the cable is approximately 22.4 ft. long, rounded to the nearest tenth.
A streetlight post needs some extra support for potential bad weather and high winds. The city wants to install metal support brackets on the light post. Each bracket will be braced into the ground and will then attach to a point on the pole that is 4.5 ft. from the ground. Each bracket is 6.5 ft. long. How far from the base of the pole should each bracket be braced in the ground? Round to the nearest tenth.(1 point)
Responses
4.7 ft.
4.7 ft.
22.0 ft.
22.0 ft.
7.9 ft.
7.9 ft.
62.5 ft.
To solve this problem, we can use the Pythagorean theorem, just like in the previous problem.
Let's call the distance from the base of the pole to where the bracket is braced in the ground "x", and the length of the bracket "b". We have:
x = ? (what we're trying to find)
b = 6.5 ft.
We also know that the bracket attaches to a point on the pole that is 4.5 ft. from the ground. This creates a right triangle with sides x (the distance from the base of the pole to where the bracket is braced in the ground), and 4.5 ft.
Using the Pythagorean theorem, we can write:
b² = x² + (4.5 ft.)²
(6.5 ft.)² = x² + (4.5 ft.)²
42.25 ft² = x² + 20.25 ft²
42.25 ft² - 20.25 ft² = x²
22 ft² = x²
Taking the square root of both sides, we get:
x = √(22 ft²)
x ≈ 4.7 ft.
Therefore, each bracket should be braced in the ground approximately 4.7 ft. from the base of the pole, rounded to the nearest tenth.