  We consider the classical limit of the recently obtained exact result for the
anomalous dimension of a cusped Wilson line with the insertion of an operator
with L units of R-charge at the cusp in planar N=4 SYM. The classical limit
requires taking both the 't Hooft coupling and L to infinity. Since the formula
for the cusp anomalous dimension involves determinants of size proportional to
L, the classical limit requires a matrix model reformulation of the result. We
construct such matrix model-like representation and find corresponding
classical algebraic curve. Using this we derive the classical value of the cusp
anomalous dimension and the 1-loop correction to it. We check our results
against the energy of the classical solution and numerically by extrapolating
from the quantum regime of finite L.
