A streetlight post needs 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 braced into the ground and will then attach to the point on the pole that is 4.5 feet from the ground each bracket is 6.5 feet long how far from the base of the pool should each bracket be braced in the ground
To find out how far from the base of the pole each bracket should be braced in the ground, we need to calculate the distance from the base to the point of attachment on the pole, taking into account the height of the bracket.
Let's call the distance from the base to the point of attachment on the pole x. So, the total length from the base to the attachment point on the pole would be x + 4.5 feet (due to the 4.5 feet from the ground to the attachment point).
The length of the bracket is 6.5 feet. Since the bracket is braced into the ground, the vertical length from the ground to the attachment point on the pole would be 6.5 feet.
From this, we can create the following equation based on the Pythagorean theorem:
(x + 4.5)^2 = x^2 + 6.5^2
Expanding and simplifying the equation:
x^2 + 9x + 20.25 = x^2 + 42.25
Subtracting x^2 from both sides:
9x + 20.25 = 42.25
Subtracting 20.25 from both sides:
9x = 22
Dividing both sides by 9:
x = 22/9
Therefore, each bracket should be braced approximately 2.44 feet (or about 2 feet and 5.32 inches) from the base of the pole.