Question

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)
Responses

62.5 ft.
62.5 ft.

7.9 ft.
7.9 ft.

22.0 ft.
22.0 ft.

4.7 ft.

Answer 1

To find how far from the base of the pole each bracket should be braced into the ground, we can use the Pythagorean theorem.

We have:
- The length of each bracket (the hypotenuse) = 6.5 ft,
- The height at which the bracket attaches to the pole (one leg of the right triangle) = 4.5 ft.

Let \( x \) be the distance from the base of the pole to the point where the bracket is braced into the ground (the other leg of the right triangle). According to the Pythagorean theorem:

\[
a^2 + b^2 = c^2
\]

where:
- \( a = 4.5 \) ft (the vertical leg),
- \( b = x \) (the horizontal leg),
- \( c = 6.5 \) ft (the hypotenuse).

Plugging in the values:

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

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

\[
20.25 + x^2 = 42.25
\]

Now, subtract \( 20.25 \) from both sides:

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

Taking the square root of both sides:

\[
x = \sqrt{22} \approx 4.7 \text{ ft}
\]

Therefore, the distance from the base of the pole to the point where each bracket should be braced into the ground is approximately **4.7 ft**.

So, the correct answer is:

**4.7 ft.**