A street light 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 attached to a point on the pole that is 4 and 1/2 ft from the ground each bracket is 6.5 ft long how far from the base of the poles in each bracket embraced in the ground round to the nearest tenth 62.5 22.0 7.9 4.7
To solve this problem, 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 in the ground as x.
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the length of the bracket, which is 6.5 ft.
The vertical side is the distance from the point on the pole (4.5 ft from the ground) to the ground, which is (x - 4.5) ft.
The horizontal side is the distance from the base of the pole to the point where the bracket braces in the ground, which is x ft.
Using the Pythagorean theorem, we have:
(6.5)^2 = (x - 4.5)^2 + x^2
42.25 = x^2 - 9x + 20.25 + x^2
2x^2 - 9x + 22 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = -9, and c = 22. Substitute these values into the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(2)(22))) / (2(2))
x = (9 ± √(81 - 176)) / 4
x = (9 ± √(-95)) / 4
Since the square root of a negative number is not a real number, there are no real solutions to this equation. This means that it is not possible to install the metal support brackets to provide the desired extra support for potential bad weather and high winds.