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)
○ 7.9 ft
○ 22.0 ft
○ 62.5 ft
○ 4.7 ft

Explanation:

Step1: Identify the right triangle

We have a right triangle where the height (from ground to bracket on pole) is \( a = 4.5 \) ft, the hypotenuse (length of the bracket) is \( c = 6.5 \) ft, and we need to find the base \( b \) (distance from base of pole to ground brace).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \( a^2 + b^2 = c^2 \). Rearranging for \( b \), we get \( b = \sqrt{c^2 - a^2} \).

Step3: Substitute the values

Substitute \( a = 4.5 \) and \( c = 6.5 \) into the formula:
\( b = \sqrt{6.5^2 - 4.5^2} \)
First, calculate \( 6.5^2 = 42.25 \) and \( 4.5^2 = 20.25 \).

Step4: Simplify the expression

Subtract the squares: \( 42.25 - 20.25 = 22 \). Then take the square root: \( b = \sqrt{22} \approx 4.7 \) (rounded to the nearest tenth).

Answer:

4.7 ft