To find the length of the support cable, we can use the Pythagorean theorem. In this scenario, we have a right triangle where:
- The height from the ground to where the cable is attached to the pole is \(20\) ft.
- The distance from the base of the pole to where the cable is anchored on the ground is \(10\) ft.
- The cable itself is the hypotenuse of the triangle.
According to the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \(c\) is the length of the cable,
- \(a\) is the height of the pole (20 ft),
- \(b\) is the distance from the pole to the anchor point on the ground (10 ft).
Now, we can substitute the values into the equation:
\[ c = \sqrt{(20)^2 + (10)^2} \] \[ c = \sqrt{400 + 100} \] \[ c = \sqrt{500} \] \[ c \approx 22.4 \text{ ft} \]
So, the length of the cable is approximately 22.4 ft.
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