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.
a. 4.7 ft
b. 7.9 ft.
c. 62.5 ft.
d. 22.0 ft.
To solve this problem, we can use the Pythagorean Theorem. The length of the bracket represents the hypotenuse of a right triangle, and the distance from the base of the pole to the brace in the ground represents one of the legs of the right triangle.
Let's call the distance from the base of the pole to the brace in the ground x. Using the Pythagorean Theorem, we can write the equation:
x^2 + 4.5^2 = 6.5^2
Simplifying the equation, we get:
x^2 + 20.25 = 42.25
Subtracting 20.25 from both sides, we get:
x^2 = 22
Taking the square root of both sides, we get:
x ≈ 4.7
Rounding to the nearest tenth, the distance from the base of the pole to the brace in the ground should be approximately 4.7 ft.
Therefore, the correct answer is:
a. 4.7 ft.