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.
7.9 ft.
7.9 ft.
62.5 ft.
62.5 ft.
4.7 ft.
To find the distance from the base of the pole where each bracket should be braced in the ground, we can use the Pythagorean theorem. The length of the bracket is the hypotenuse of a right triangle, and the height from the ground to the point where the bracket attaches to the pole is one side of the triangle. The distance from the base of the pole to where the bracket should be braced in the ground is the other side of the triangle.
Using the Pythagorean theorem: c^2 = a^2 + b^2
c = 6.5 ft. (length of the bracket)
a = 4.5 ft. (height from the ground to the point where the bracket attaches to the pole)
b = distance from the base of the pole to where the bracket should be braced in the ground (unknown)
Solving for b:
c^2 = a^2 + b^2
(6.5)^2 = (4.5)^2 + b^2
42.25 = 20.25 + b^2
b^2 = 22
b ≈ 4.7 ft.
Therefore, each bracket should be braced in the ground approximately 4.7 ft. from the base of the pole.