Answer
$\frac{241}{8}\ ft$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the length of the wire and the height is 4 foot shorter, or $x-4$
Step 2. Using the Pythagorean's Theorem in the right triangle, we have $(x-4)^2+15^2=x^2$ or $x^2-8x+16+225=x^2$, which gives $8x=241$
Step 3. Thus, we have $x=\frac{241}{8}\ ft$
