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 7.9 ft. 7.9 ft. 22.0 ft. 22.0 ft. 4.7 ft. 4.7 ft. 62.5 ft. 62.5 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 scenario, we have a right triangle where:
- The height from the ground to the attachment point on the pole is one leg (4.5 ft).
- The length of the bracket is the hypotenuse (6.5 ft).
- The distance from the base of the pole to where the bracket is braced in the ground is the other leg.

Let \( x \) be the distance from the base of the pole to where the bracket is braced. 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 substitute these values into the equation:

\[ x^2 + 20.25 = 42.25 \]

Now, solve for \( x^2 \):

\[ x^2 = 42.25 - 20.25 \]

\[ x^2 = 22 \]

Now take the square root of both sides to find \( x \):

\[ x = \sqrt{22} \]

Calculating the square root:

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

Thus, the distance from the base of the pole to where each bracket is braced in the ground is approximately **4.7 ft**.