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)

.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. The bracket is 6.5 ft long and attaches to a point on the pole that is 4.5 ft from the ground. This forms a right triangle.

Using the Pythagorean theorem:
x^2 + 4.5^2 = 6.5^2
x^2 + 20.25 = 42.25
x^2 = 22
x = √22
x ≈ 4.7 ft

Therefore, each bracket should be braced in the ground at a distance of approximately 4.7 ft from the base of the pole.