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?
Since the wire is 34 feet long, the distance from the center anchor to the top of each pole is $\frac{34}{2}=17$ feet, so $x=\boxed{17}$. [asy]
unitsize(0.25cm);
pair A=(3,0), B=(33,0), C=(18,24), D=(18,0);
draw(A--C--B); draw(C--D,dotted+linewidth(0.7));
label("17",(A+C)/2,W); label("17",(C+B)/2,E); label("x", (D+(18,B.y))/2, S);
dot(A); dot(B); dot(C); dot(D);
[/asy]