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)Responses

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. The bracket forms a right triangle where one leg is the height from the ground to the point on the pole where the bracket attaches (4.5 ft), and the other leg is the distance from the base of the pole to the brace in the ground (let's call this distance \(x\)). The hypotenuse is the length of the bracket (6.5 ft).

According to the Pythagorean theorem:

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

Here:

• \(a = 4.5\) ft (the height),
• \(b = x\) (the distance from the base of the pole),
• \(c = 6.5\) ft (the length of the bracket).

Substituting these values into the equation gives:

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

Calculating the squares:

\[ 20.25 + x^2 = 42.25 \]

Now, isolate \(x^2\):

\[ x^2 = 42.25 - 20.25 \]

\[ x^2 = 22 \]

Now, take the square root of both sides to find \(x\):

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

Rounding to the nearest tenth, we find:

\[ x \approx 4.7 \]

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