To determine the length of the cable, we can use the Pythagorean theorem. The situation can be visualized as a right triangle where:
- One leg (the vertical leg) is the height from the ground to where the cable is attached to the pole, which is 20 ft.
- The other leg (the horizontal leg) is the distance from the base of the pole to the point where the cable is anchored on the ground, which is 10 ft.
- The hypotenuse represents the length of the cable.
According to the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]
Where:
- \( c \) is the length of the cable,
- \( a \) is the vertical leg (20 ft), and
- \( b \) is the horizontal leg (10 ft).
Now we can substitute the values: \[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \]
Now, take the square root of both sides to find \( c \): \[ c = \sqrt{500} \] \[ c \approx 22.4 , \text{ft} \]
Rounding to the nearest tenth, the length of the cable is approximately 22.4 ft.
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