The 20 feet long cable is attached from the top of the vertical pole to a point on the ground, 16 feet away from the base of the pole. How tall is the pole, and if it costs $⁢2 per foot to paint the pole, what is the total cost?

The pole, ground, and cable form a right triangle, with the 20-foot cable as the hypotenuse and the ground distance of 16 feet as one leg. By the Pythagorean theorem, the pole’s height is √(20² − 16²) = √144 = 12 feet. Painting costs $2 per foot, so 12 × $2 = $24; this matches the choice saying the pole is 12 feet tall and costs 24 dollars.

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