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.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.