To solve this problem, we can use the Pythagorean theorem. The length of the bracket will be the hypotenuse of a right triangle, while the vertical distance from the ground to the point where the bracket attaches to the pole will be one leg, and the horizontal distance from the base of the pole to where the bracket is braced into the ground will be the other leg of the triangle.
Let's denote:
- The length of the bracket (the hypotenuse) as \( c = 6.5 \) ft.
- The height of the attachment point on the pole (one leg of the triangle) as \( a = 4.5 \) ft.
- The horizontal distance from the base of the pole to where the bracket is braced in the ground (the other leg of the triangle) as \( b \).
According to the Pythagorean theorem, we have:
\[ c^2 = a^2 + b^2 \]
Substituting the values we have to find \( b \):
\[ (6.5)^2 = (4.5)^2 + b^2 \]
Calculating \( c^2 \) and \( a^2 \):
\[ 42.25 = 20.25 + b^2 \]
Now, solving for \( b^2 \):
\[ b^2 = 42.25 - 20.25 \] \[ b^2 = 22 \]
Taking the square root of both sides:
\[ b = \sqrt{22} \approx 4.7 \text{ ft} \]
Therefore, the distance from the base of the pole to where each bracket should be braced in the ground is approximately 4.7 ft.
So, the correct answer is 4.7 ft.
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