The diffraction by a composite wedge composed of a perfect conductor and a lossy dielectric is investigated using the hidden rays of diffraction (HRD) method. The usual principle of geometrical optics is employed to trace not only ordinary rays incident on the lit boundary but also hidden rays incident on the shadow boundary. The modified propagation constants are adopted to represent the non-uniform plane wave transmission through the lossy dielectric. The HRD diffraction coefficients are constructed routinely by the sum of the cotangent functions, which have one-to-one correspondence with both ordinary and hidden rays. The angular period of the cotangent functions is adjusted to satisfy the edge condition at the tip of the composite wedge. The accuracy of the HRD diffraction coefficients in the physical region is checked by showing how closely the diffraction coefficients in the complementary region satisfy the null-field condition.