### Instruction: The bottoms of two vertical poles are 12 feet apart and are on a region of flat ground. One pole is 6 feet tall and the other is 15 feet tall. How long, in feet, is a wire stretched from the top of one pole to the top of the other pole?### Response: I need to find the length of the wire, which is the hypotenuse of a right triangle whose legs are the difference in height of the poles and the distance between them.
I can use the Pythagorean theorem to find the length of the hypotenuse: c^2 = a^2 + b^2, where c is the length of the wire, a is the difference in height of the poles, and b is the distance between them.
I can plug in the given values into the formula: c^2 = (15 - 6)^2 + 12^2
I can simplify the expression: c^2 = 9^2 + 12^2
I can evaluate the squares: c^2 = 81 + 144
I can add the terms: c^2 = 225
I can take the square root of both sides: c = sqrt(225)
I can simplify the radical: c = 15