a streetlight post needs some extra support for potenial 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. 62.5 ft
b. 7.9 ft
c. 22.0 ft
d. 4.7 ft
To find the distance from the base of the pole that each bracket should be braced in the ground, we can use the Pythagorean theorem. Let x be the distance from the base of the pole to the point where each bracket is braced in the ground.
According to the Pythagorean theorem, we have:
x^2 + 4.5^2 = 6.5^2
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides, we get:
x ≈ √22
x ≈ 4.7 ft
Therefore, each bracket should be braced in the ground about 4.7 ft from the base of the pole.
So the correct answer is option d. 4.7 ft.