Use the Pythagorean Theorem Quick Check

Question

4 of 54 of 5 Items

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

7.9 ft.
7.9 ft.

62.5 ft.
62.5 ft.

4.7 ft.
4.7 ft.

22.0 ft.

Answer 1

To find out how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean Theorem. The setup forms a right triangle where:

• One leg (height) is the vertical distance from the ground to the bracket attachment point on the pole, which is 4.5 ft.
• The other leg (distance from the pole) is what we want to find.
• The hypotenuse is the length of the bracket, which is 6.5 ft.

According to the Pythagorean Theorem:

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

where:

• \(a\) is the height (4.5 ft),
• \(b\) is the distance from the pole (which we are trying to find),
• \(c\) is the length of the bracket (6.5 ft).

Rearranging the formula to solve for \(b\):

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

Substituting the known values:

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

Calculating the squares:

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

Taking the square root to find \(b\):

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

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

So, the correct response is:

4.7 ft.