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 postEach bracket will be braced into the ground and will then attach to a point on the pole that is 4.5 ftfrom the groundEach bracket is 6.5 ftlong How far from the base of the pole should each bracket be braced in the ground ? Round to the nearest tenth(1 point )
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 each bracket will be braced in the ground as 'x'. We need to find the value of 'x'.
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the distance from the base of the pole to the point on the pole attached to the bracket, which is 4.5 ft.
The other two sides are x (the distance from the base of the pole to the point where the bracket is braced in the ground) and 6.5 ft (the length of each bracket).
So, we have the equation:
x^2 + 6.5^2 = 4.5^2
Simplifying the equation:
x^2 + 42.25 = 20.25
Subtracting 42.25 from both sides of the equation:
x^2 = 20.25 - 42.25
x^2 = 22
Taking the square root of both sides of the equation:
x = sqrt(22)
Rounding to the nearest tenth:
x ≈ 4.7 ft.
Therefore, each bracket should be braced approximately 4.7 feet from the base of the pole.