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?
Let's call the distance between the two bottoms of the poles $x$. The distance between the two bottoms of the poles is 12 feet, so $x=12$. So the horizontal distance between the two poles is the base of the right triangle. And the difference in the heights of the poles is the height of the right triangle. The base of the right triangle is $x=12$. And the height of the right triangle is $15-6=9$. So now we need to find the length of the hypotenuse of a right triangle with base 12 and height 9. We can use the Pythagorean Theorem for that: $c^2=a^2+b^2$. We need to solve for $c$: $c=\sqrt{a^2+b^2}$. So $c=\sqrt{12^2+9^2}$. Which is $\sqrt{144+81}$. And that is $\sqrt{225}$. Which is 15. So the wire is 15 feet long.

