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.
4.7 ft.
4.7 ft.
62.5 ft.
62.5 ft.
7.9 ft.
The distance from the base of the pole should be braced in the ground can be found using the Pythagorean theorem.
Let x be the distance from the base of the pole to where the bracket is braced in the ground.
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 ≈ 4.7 ft.
Therefore, each bracket should be braced in the ground approximately 4.7 ft. from the base of the pole.