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)

22.0 ft.
62.5 ft
4.7 ft.
7.9 ft.

Answer 1

To find out how far from the base of the pole each bracket should be braced into the ground, we can think of the bracket as forming a right triangle with the pole and the ground.

Here are the details we know:
- The height from the ground to the point on the pole where the bracket attaches is 4.5 ft.
- The length of the bracket (the hypotenuse of the triangle) is 6.5 ft.
- We need to find the distance from the base of the pole to where the bracket is braced into the ground (the adjacent side of the triangle).

We can use the Pythagorean theorem to find the distance (denote it as \( x \)):
\[
x^2 + 4.5^2 = 6.5^2
\]

First, calculate \( 4.5^2 \) and \( 6.5^2 \):
\[
4.5^2 = 20.25
\]
\[
6.5^2 = 42.25
\]

Now plug these values into the equation:
\[
x^2 + 20.25 = 42.25
\]

Subtract \( 20.25 \) from both sides:
\[
x^2 = 42.25 - 20.25
\]
\[
x^2 = 22
\]

Now take the square root of both sides to find \( x \):
\[
x = \sqrt{22} \approx 4.7 \text{ ft (rounded to the nearest tenth)}
\]

Thus, the distance from the base of the pole that each bracket should be braced into the ground is approximately **4.7 ft**.