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)
22.0 ft.
○ 4.7 ft.
62.5 ft.
○ 7.9 ft.
To solve this problem, we can use 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 = 22
x ≈ 4.7 ft
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole. The correct answer is 4.7 ft.