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)

Question

Responses

62.5 ft.
62.5 ft.

22.0 ft.
22.0 ft.

7.9 ft.
7.9 ft.

4.7 ft.
4.7 ft.

Answer 1

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. In this case, we can consider the setup as a right triangle where:

• One leg is the height of the pole where the bracket attaches, which is 4.5 ft.
• The other leg is the distance from the base of the pole to the point where the bracket is anchored in the ground (which we want to find).
• The hypotenuse is the length of the bracket, which is 6.5 ft.

Let \( x \) be the distance from the base of the pole to the point where the bracket is anchored in the ground. According to the Pythagorean theorem:

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

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

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

Now we can substitute these values into the equation:

\[ x^2 + 20.25 = 42.25 \]

Subtracting 20.25 from both sides:

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

Now taking the square root of both sides:

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

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

Thus, the correct answer is:

4.7 ft.