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
62.5 ft.
62.5 ft.
22.0 ft.
22.0 ft.
4.7 ft.
4.7 ft.
7.9 ft.
To determine how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean theorem.
Let x be the distance from the base of the pole to the point where the bracket is braced in the ground.
Let y be the height at which the bracket is attached to the pole (4.5 ft).
Let z be the length of the bracket (6.5 ft).
Using the Pythagorean theorem, we have:
x^2 + y^2 = z^2
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
Rounded to the nearest tenth, x is approximately 4.7 ft.
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
The correct response is:
4.7 ft.