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
7.9 ft.
7.9 ft.
4.7 ft.
4.7 ft.
62.5 ft.
62.5 ft.
22.0 ft.
22.0 ft.
To find the distance from the base of the pole to brace the bracket in the ground, we can use the Pythagorean theorem. According to the problem, the point on the pole where the bracket attaches is 4.5 ft from the ground, and the bracket itself is 6.5 ft long.
Let's assume the distance we need to find is x.
Using the Pythagorean theorem, we can set up the equation:
x^2 + 4.5^2 = 6.5^2
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides, we get:
x ≈ √22
x ≈ 4.7 ft (rounded to the nearest tenth)
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
To solve this problem, we can use the Pythagorean theorem. We need to find the length of the hypotenuse of a right triangle, with one leg being 4.5 ft and the other leg being the distance from the base of the pole to where the bracket is braced in the ground.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
Hypotenuse^2 = 4.5^2 + (distance from base of pole)^2
Hypotenuse^2 = 20.25 + (distance from base of pole)^2
Since the length of the hypotenuse (6.5 ft) is given, we can rearrange the equation:
6.5^2 = 20.25 + (distance from base of pole)^2
42.25 = 20.25 + (distance from base of pole)^2
Subtracting 20.25 from both sides, we get:
22 = (distance from base of pole)^2
Taking the square root of both sides, we get:
√22 = distance from base of pole
Rounding to the nearest tenth, the distance from the base of the pole should be 4.7 ft.
So the correct response is:
4.7 ft.
To determine the distance from the base of the pole where each bracket should be braced in the ground, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the pole (4.5 ft.) is one of the sides, and the length of the bracket (6.5 ft.) is another side. The distance from the base of the pole to where the bracket should be braced is the remaining side.
Let's assign variables to the sides:
- Height of the pole = a = 4.5 ft.
- Length of the bracket = b = 6.5 ft.
- Distance from the base to the braced point = c (what we need to find).
Using the Pythagorean theorem:
a^2 + b^2 = c^2
Plugging in the values we have:
(4.5 ft.)^2 + (6.5 ft.)^2 = c^2
20.25 ft^2 + 42.25 ft^2 = c^2
62.5 ft^2 = c^2
To find c, we need to take the square root of both sides:
√(62.5 ft^2) = √(c^2)
7.9 ft = c
Therefore, each bracket should be braced in the ground at a distance of 7.9 ft from the base of the pole.
The correct answer is 7.9 ft.