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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the distance from the base of the pole where each bracket should be braced, we can use the Pythagorean theorem.

Let's denote the distance from the base of the pole to the point where the bracket is braced as x.

According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

In this case, the leg adjacent to the right angle is x ft, and the other leg is 4.5 ft. The hypotenuse is the length of the bracket, which is 6.5 ft.

Therefore, we can set up the equation:

x^2 + 4.5^2 = 6.5^2

Simplifying this equation gives:

x^2 + 20.25 = 42.25

Subtracting 20.25 from both sides:

x^2 = 42.25 - 20.25

x^2 = 22

Taking the square root of both sides:

x = √22

x ≈ 4.7

Therefore, each bracket should be braced in the ground approximately 4.7 ft. from the base of the pole, rounding to the nearest tenth.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the distance from the base of the pole at which each bracket should be braced in the ground, we can use the Pythagorean theorem.

Let's call the distance from the base of the pole to the point where the bracket is braced in the ground "x". We can use the Pythagorean theorem to determine the length of the hypotenuse (the length of the bracket) and then solve for "x".

According to the Pythagorean theorem, the square of the hypotenuse (the length of the bracket) is equal to the sum of the squares of the other two sides (the distance from the ground point to the bracket point and x, the distance from the base of the pole to the ground point):

(4.5^2) + (x^2) = (6.5^2)

Simplifying the equation:

20.25 + x^2 = 42.25

x^2 = 42.25 - 20.25

x^2 = 22

Taking the square root of both sides:

x = √22

x ≈ 4.7 ft

Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.

Answer 3

[AI-generated answer — Explain Bot]

To find the distance from the base of the pole where each bracket should be braced in the ground, we need to use the Pythagorean theorem.

Here's how we can break it down step by step:

1. Draw a diagram: Draw a right triangle representing the streetlight post, where the height from the base of the pole to the point where each bracket attaches is 4.5 ft and the length of each bracket is 6.5 ft.

2. Identify the values: We have the height (opposite side) of the triangle as 4.5 ft and the length of the bracket (hypotenuse) as 6.5 ft. We need to find the distance from the base of the pole to the point where each bracket should be braced (adjacent side).

3. Apply the Pythagorean theorem: According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

So, we can set up the equation:
(adjacent side)^2 + (opposite side)^2 = (hypotenuse)^2

Substituting the given values, we get:
(adjacent side)^2 + (4.5 ft)^2 = (6.5 ft)^2

4. Solve for the adjacent side: Rearranging the equation and simplifying, we have:
(adjacent side)^2 = (6.5 ft)^2 - (4.5 ft)^2

Calculating the values, we get:
(adjacent side)^2 = 42.25 ft^2 - 20.25 ft^2
(adjacent side)^2 = 22 ft^2

Taking the square root of both sides, we have:
adjacent side = sqrt(22 ft^2)

5. Calculate the final answer: Evaluating sqrt(22 ft^2) ≈ 4.7 ft (rounded to the nearest tenth).

Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.