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
22.0 ft.
22.0 ft.
4.7 ft.
4.7 ft.
7.9 ft.
7.9 ft.
62.5 ft.
62.5 ft.
Skip to navigation
To determine the distance from the base of the pole where each bracket should be braced in the ground, we can use the Pythagorean Theorem.
Let's denote the distance from the base of the pole to the point where each bracket is braced in the ground as x.
According to the problem, each bracket is 6.5 ft long and attaches to a point on the pole that is 4.5 ft from the ground.
Using the Pythagorean Theorem, we have:
x^2 + 4.5^2 = 6.5^2
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
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.
The correct answer is 4.7 ft.
To determine how far from the base of the pole 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 have a right triangle, where the length of the bracket (6.5 ft.) is the hypotenuse, and the vertical segment from the ground to the point on the pole (4.5 ft.) is one of the legs.
Using the Pythagorean theorem, we have:
x^2 + 4.5^2 = 6.5^2
Simplifying the equation:
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 = sqrt(22)
Rounding to the nearest tenth:
x ≈ 4.7 ft.
Therefore, each bracket should be braced approximately 4.7 ft. from the base of the pole. The correct answer is:
4.7 ft.
To solve this problem, we need to use the concept of similar triangles.
First, let's draw a diagram of the streetlight post with the metal support brackets. The distance from the base of the pole to the point where the bracket is braced into the ground will be our unknown, which we'll call "x."
___________
| |
| |
| |
| x | <-- distance from base to brace in the ground
| | |
| |
|__________|
/\ /\
/ \ / \
/ \ / \
/______\/______\ <-- 4.5 ft from the ground
Now, let's create two similar triangles: one with the full length of the bracket and the other with just the part above the ground.
Since we know that each bracket is 6.5 ft long and that the point on the pole where it attaches is 4.5 ft from the ground, we have the following ratios:
x / 4.5 = (6.5 - x) / 6.5
Cross-multiplying and simplifying, we get:
6.5x = 4.5 * (6.5 - x)
6.5x = 29.25 - 4.5x
11x = 29.25
x ≈ 2.659 (rounded to the nearest tenth)
Therefore, the distance from the base of the pole to where each bracket should be braced in the ground is approximately 2.7 ft.
So the correct answer is 2.7 ft.