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

22.0 ft.
22.0 ft.

62.5 ft.
62.5 ft.

4.7 ft.
4.7 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 visualize the situation as a right triangle where:

• The height from the ground to where the bracket attaches to the pole (4.5 ft) is one leg of the triangle.
• The length of the bracket (6.5 ft) is the hypotenuse.
• The distance from the base of the pole to the point where the bracket is braced in the ground is the other leg of the triangle, which we need to find.

Using the Pythagorean theorem, which states that \( a^2 + b^2 = c^2 \) (where \( c \) is the hypotenuse and \( a \) and \( b \) are the legs of the triangle), we can set up the equation:

Let \( x \) be the distance from the base of the pole to the point where the bracket is braced in the ground.

So, we have:

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

Calculating the squares:

\[ 20.25 + x^2 = 42.25 \]

Subtracting \( 20.25 \) from both sides:

\[ x^2 = 42.25 - 20.25 \]

\[ x^2 = 22 \]

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

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

Rounding to the nearest tenth, we find:

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

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