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)

To find out how far from the base of the pole each bracket should be braced in the ground, you can use the Pythagorean theorem. In this scenario, you have a right triangle where:

- One leg (the height of the pole where the bracket attaches) is 4.5 ft.
- The hypotenuse (the length of the bracket) is 6.5 ft.
- The other leg (the distance from the base of the pole where the bracket is braced into the ground) is what we need to find.

We can denote the distance from the base of the pole as \(x\). According to the Pythagorean theorem:

\[
x^2 + (4.5)^2 = (6.5)^2
\]

Calculating \( (4.5)^2 \) and \( (6.5)^2 \):

\[
(4.5)^2 = 20.25
\]
\[
(6.5)^2 = 42.25
\]

Plugging these values into the equation:

\[
x^2 + 20.25 = 42.25
\]

Now, subtract 20.25 from both sides:

\[
x^2 = 42.25 - 20.25
\]
\[
x^2 = 22
\]

Now, we take the square root of both sides to solve for \(x\):

\[
x = \sqrt{22} \approx 4.69 \text{ ft.}
\]

Rounding this to the nearest tenth gives:

\[
x \approx 4.7 \text{ ft.}
\]

Therefore, the correct answer is:

**4.7 ft.**