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.
7.9 ft.
7.9 ft.
22.0 ft.
22.0 ft.
62.5 ft.
To find the distance from the base of the pole to where each bracket should be braced in the ground, we can use the Pythagorean theorem.
Let's call the distance from the base of the pole to where each bracket should be braced in the ground "x".
Using the Pythagorean theorem, we can set up the following equation:
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 = 22
Taking the square root of both sides:
x = √22
x ≈ 4.69 ft. (rounded to the nearest tenth)
So each bracket should be braced in the ground approximately 4.7 ft. from the base of the pole.