From the diagram provided in the question, we have the following triangle:
We have the following angle and side measures:

Recall the Sine Rule:

Comparing to our triangle, we have the sine rule applied as:

Length of Longer Wire (L):

Substituting the given values, we have:

The length of the longer wire is approximately 10.6 feet.
Length of Shorter Wire (S):

Substituting known values, we have:

The length of the shorter wire is approximately 7.8 feet.