Use the Pythagorean Theorem Quick Check

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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.

22.0 ft.
22.0 ft.

62.5 ft.
62.5 ft.

4.7 ft.
4.7 ft.
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Answer 1

To find how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This theorem can be expressed as:

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

In this scenario:

• The length of the bracket (hypotenuse) is 6.5 ft (c = 6.5).
• The height from the ground to the point where the bracket attaches to the pole (one side) is 4.5 ft (b = 4.5).
• We need to find the distance from the base of the pole to the point where the bracket is braced in the ground (the other side, a).

Using the theorem, we can rearrange it to find \( a \):

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

Now, substitute the values:

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

Calculating the squares:

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

Now take the square root:

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

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

So the correct answer is: 4.7 ft.