Question

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 62.5 ft. 62.5 ft. 4.7 ft. 4.7 ft. 22.0 ft. 22.0 ft. 7.9 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. The length of the bracket acts as the hypotenuse of a right triangle, while the height from the ground to where the bracket is attached to the pole (4.5 ft) serves as one leg of that triangle.

Let \( d \) be the distance from the base of the pole to where the bracket is braced in the ground. According to the Pythagorean theorem:

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

Calculating \( (4.5)^2 \) and \( (6.5)^2 \):

\[ d^2 + 20.25 = 42.25 \]

Now, subtract \( 20.25 \) from both sides:

\[ d^2 = 42.25 - 20.25 \]

This simplifies to:

\[ d^2 = 22 \]

Taking the square root of both sides gives:

\[ d = \sqrt{22} \approx 4.69 \]

Rounding this to the nearest tenth gives:

\[ d \approx 4.7 \]

Therefore, the distance from the base of the pole should be 4.7 ft.