To find the length of the cable, we can visualize the situation as a right triangle. The height of the pole where the cable is attached is one leg of the triangle, the distance from the base of the pole to the anchor point on the ground is the other leg, and the cable itself is the hypotenuse.
Given:
- Height of the pole where the cable is attached: \( 20 \) ft (vertical leg)
- Distance from the base of the pole to the anchor point: \( 10 \) ft (horizontal leg)
We can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (cable length) is equal to the sum of the squares of the other two sides:
\[ c^2 = a^2 + b^2 \]
Where:
- \( c \) is the length of the cable
- \( a = 20 \) ft (height)
- \( b = 10 \) ft (horizontal distance)
Substituting in the values:
\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \]
Now, taking the square root to find \( c \):
\[ c = \sqrt{500} \] \[ c = \sqrt{100 \times 5} \] \[ c = 10\sqrt{5} \]
Calculating \( \sqrt{5} \):
\[ \sqrt{5} \approx 2.236 \]
Thus,
\[ c \approx 10 \times 2.236 \approx 22.36 \]
Rounding to the nearest tenth, the length of the cable is approximately:
\[ \boxed{22.4} \text{ ft} \]
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