To determine how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean theorem.
We know:
- The length of the bracket (hypotenuse) is 6.5 ft.
- The height at which the bracket is attached to the pole (vertical leg) is 4.5 ft.
We need to find the distance from the base of the pole (horizontal leg). We can denote this distance as \( x \).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the height of the attachment (4.5 ft),
- \( b \) is the distance from the base of the pole (x),
- \( c \) is the length of the bracket (6.5 ft).
Plugging in the values:
\[ (4.5)^2 + x^2 = (6.5)^2 \]
Calculating the squares:
\[ 20.25 + x^2 = 42.25 \]
Now, we can isolate \( x^2 \):
\[ x^2 = 42.25 - 20.25 \] \[ x^2 = 22 \]
Now, take the square root to find \( x \):
\[ x = \sqrt{22} \approx 4.69 \]
Rounding to the nearest tenth, we get:
\[ x \approx 4.7 \]
So the distance from the base of the pole should be approximately 4.7 ft.