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)
22.0 ft.
7.9 ft.
62.5 ft.
4.7 ft.

1 answer

To solve this problem, we can use the Pythagorean theorem. The length of the bracket will be the hypotenuse of a right triangle, while the vertical distance from the ground to the point where the bracket attaches to the pole will be one leg, and the horizontal distance from the base of the pole to where the bracket is braced into the ground will be the other leg of the triangle.

Let's denote:

  • The length of the bracket (the hypotenuse) as \( c = 6.5 \) ft.
  • The height of the attachment point on the pole (one leg of the triangle) as \( a = 4.5 \) ft.
  • The horizontal distance from the base of the pole to where the bracket is braced in the ground (the other leg of the triangle) as \( b \).

According to the Pythagorean theorem, we have:

\[ c^2 = a^2 + b^2 \]

Substituting the values we have to find \( b \):

\[ (6.5)^2 = (4.5)^2 + b^2 \]

Calculating \( c^2 \) and \( a^2 \):

\[ 42.25 = 20.25 + b^2 \]

Now, solving for \( b^2 \):

\[ b^2 = 42.25 - 20.25 \] \[ b^2 = 22 \]

Taking the square root of both sides:

\[ b = \sqrt{22} \approx 4.7 \text{ ft} \]

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

So, the correct answer is 4.7 ft.