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.
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.
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