Question

A streetlight needs some extra support for potential bad weather and high winds. The city to install metal support brackets on the light post. Each bracket will be braced into the ground and will 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. (4.7 ft; 7.9 ft)

Answer 1

To find the distance from the base of the pole where each bracket should be braced in the ground, we can use the Pythagorean theorem. In this scenario, we have:

- The height from the ground to the attachment point on the pole: \( h = 4.5 \) ft
- The length of the bracket: \( b = 6.5 \) ft
- The distance from the base of the pole to where the bracket is anchored in the ground: \( d \) (this is what we need to find)

According to the Pythagorean theorem, we can relate these three measurements as follows:

\[
b^2 = h^2 + d^2
\]

Substituting the known values into the equation:

\[
(6.5)^2 = (4.5)^2 + d^2
\]
\[
42.25 = 20.25 + d^2
\]

Now we will solve for \( d^2 \):

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

Now we take the square root to find \( d \):

\[
d = \sqrt{22} \approx 4.690
\]

Rounding to the nearest tenth, we get:

\[
d \approx 4.7 \text{ ft}
\]

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