Two vertical poles are placed 30 feet apart, and the top of each pole is x feet above ground. The ends of a wire 34 feet in length are attached at the tops of the poles and its center is anchored to the ground halfway between the poles, as shown. What is the value of x?
Drawing the scenario given, we see that we have a trapezoid with side lengths 30 and 34. Since $x$ is the distance between the ground and the tops of the poles, $x$ is the height of the trapezoid. We also see that the height of the trapezoid and the distance from the center of the trapezoid to a base form a right triangle such that \[(17)^2+x^2=15^2.\] Simplifying, we find that $289+x^2=225$. Solving for $x$ gives us the answer of $x=\boxed{8}$. [asy]
draw((0,0)--(30,0)--(15,8)--cycle);
draw((15,0)--(15,8));
label("15",(0,0)--(15,0),S);
label("17",(15,0)--(30,0),S);
label("17",(0,0)--(15,8),NW);
label("15",(15,0)--(15,8),W);
[/asy]