To find out how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean Theorem. The setup forms a right triangle where:
- One leg (height) is the vertical distance from the ground to the bracket attachment point on the pole, which is 4.5 ft.
- The other leg (distance from the pole) is what we want to find.
- The hypotenuse is the length of the bracket, which is 6.5 ft.
According to the Pythagorean Theorem:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) is the height (4.5 ft),
- \(b\) is the distance from the pole (which we are trying to find),
- \(c\) is the length of the bracket (6.5 ft).
Rearranging the formula to solve for \(b\):
\[ b^2 = c^2 - a^2 \]
Substituting the known values:
\[ b^2 = (6.5)^2 - (4.5)^2 \]
Calculating the squares:
\[ b^2 = 42.25 - 20.25 \] \[ b^2 = 22 \]
Taking the square root to find \(b\):
\[ b = \sqrt{22} \approx 4.7 \text{ ft} \]
Therefore, the distance from the base of the pole that each bracket should be braced in the ground is approximately 4.7 ft.
So, the correct response is:
4.7 ft.