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, we can use the Pythagorean theorem.

Let:

• \( h \) be the vertical height from the ground to the point where the bracket is attached, which is 4.5 ft.
• \( l \) be the length of the bracket, which is 6.5 ft.
• \( d \) be the distance from the base of the pole to where the bracket is braced in the ground.

According to the Pythagorean theorem:

\[ l^2 = h^2 + d^2 \]

Plugging in the values:

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

Calculating the squares:

\[ 42.25 = 20.25 + d^2 \]

Now, subtract the height squared from the length squared:

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

Now, take the square root to find \( d \):

\[ d = \sqrt{22} \approx 4.69 \]

Rounding to the nearest tenth gives:

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

So, the distance from the base of the pole to where each bracket should be braced in the ground is approximately 4.7 ft.