Street light post need some extra support for potential bad weather and Highwinds. The city wants to install metal support brackets on the light post. Each bracket will be placed into the ground and will then attach to a point on the pool that is 4.5 feet from the ground each bracket is 6.5 feet long how far from the base of a pole should each bracket be breast to the ground round to the nearest 10th?
To find the distance from the base of the pole where each bracket should be attached to the ground, we can use the Pythagorean theorem.
Let x be the distance from the base of the pole where each bracket should be attached to the ground. According to the problem, each bracket is 6.5 feet long and attaches to a point on the pole that is 4.5 feet from the ground. Therefore, the distance from the attachment point to the ground is the hypotenuse of a right triangle with sides x and 4.5 feet.
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 ≈ 4.69 (rounded to the nearest 10th)
Therefore, each bracket should be attached to the ground approximately 4.7 feet from the base of the pole.