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)

Question

Responses

7.9 ft.

62.5 ft.

4.7 ft.

22.0 ft.

Answer 1

To determine how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean theorem. In this scenario, the length of the bracket serves as the hypotenuse of a right triangle, while the vertical distance from the ground to the attachment point on the pole (4.5 ft) is one leg, and the distance from the base of the pole to where the bracket is braced in the ground is the other leg.

Let's denote:

• Length of the bracket (hypotenuse) = \( c = 6.5 \) ft
• Height of the attachment point (one leg) = \( a = 4.5 \) ft
• Distance from the base of the pole to where the bracket is braced in the ground (the other leg) = \( b \)

According to the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] Substituting the known values: \[ (4.5)^2 + b^2 = (6.5)^2 \] Calculating the squares: \[ 20.25 + b^2 = 42.25 \] Now, isolate \( b^2 \): \[ b^2 = 42.25 - 20.25 \] \[ b^2 = 22 \] Now, take the square root of both sides to find \( b \): \[ b = \sqrt{22} \approx 4.7 \text{ ft} \]

Thus, the distance from the base of the pole to where the bracket should be braced in the ground is approximately 4.7 ft.

The correct answer is 4.7 ft.