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
22.0 ft.
22.0 ft.
62.5 ft.
62.5 ft.
7.9 ft.
7.9 ft.
4.7 ft.
To find the distance from the base of the pole that each bracket should be braced in the ground, we can use the Pythagorean theorem. In this case, the height of the pole is 4.5 ft, and the length of the bracket is 6.5 ft.
Let's call the distance from the base of the pole to the point of bracing in the ground "x".
Using the Pythagorean theorem, we have:
x^2 + 4.5^2 = 6.5^2
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
x ≈ √22
x ≈ 4.69 ft
Rounding to the nearest tenth, each bracket should be braced in the ground at a distance of 4.7 ft from the base of the pole.
Therefore, the correct response is 4.7 ft.
To solve this problem, we can use the Pythagorean theorem. According to the problem, each bracket is 6.5 ft long and attaches to a point on the pole that is 4.5 ft from the ground. Let's denote the distance from the base of the pole to the point where the bracket attaches as 'x'.
Now, let's consider a right-angled triangle where the two legs represent the height of the pole from the ground (4.5 ft) and the distance from the base of the pole to the point where the bracket attaches (x ft), and the hypotenuse represents the length of the bracket (6.5 ft).
According to the Pythagorean theorem, the square of the length of the hypotenuse (6.5 ft) is equal to the sum of the squares of the lengths of the other two sides:
(4.5 ft)^2 + (x ft)^2 = (6.5 ft)^2
We can now solve this equation to find the value of x:
(4.5)^2 + x^2 = (6.5)^2
20.25 + x^2 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
x = sqrt(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. Hence, the correct answer is 4.7 ft.