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)
O 4.7 ft.
O 7.9 ft.
• 22.0 ft.
• 62.5 ft.
To solve this problem, we can use the Pythagorean theorem.
Let's consider the light post, the ground, and the point where the bracket is attached as a right-angled triangle.
The length of the bracket, which acts as the hypotenuse, is 6.5 ft.
The height of the bracket from the ground to the point where it is attached to the pole is given as 4.5 ft.
Let's assume that the distance from the base of the pole to the point where the bracket is braced in the ground is represented by 'x' ft.
Using the Pythagorean theorem, we have:
(x^2) + (4.5^2) = (6.5^2)
Simplifying this equation:
x^2 + 20.25 = 42.25
Subtracting 20.25 from both sides:
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides:
x = √22
Calculating the approximate value of √22, we find:
x ≈ 4.69 ft.
Therefore, the distance from the base of the pole to where each bracket should be braced in the ground is approximately 4.7 ft.
The correct answer is option O 4.7 ft.