We have used HST-WFPC2 multiband observations of a field around SN 1987A in the Large Magellanic Cloud to measure its distance from the Sun . The observations allowed us to carefully determine the interstellar extinction along the line of sight to a large number of stars and to measure the LMC distance by using two stellar distance indicators : the Red Clump and the Tip of the Red Giant Branch . From an application of the Red Clump method we obtain a distance modulus ( m - M ) _ { 0 ,RC } ^ { LMC } =18.59 \pm 0.04 \pm 0.08 mag ( statistical plus systematic error ) , in good agreement with the distance derived by using the Tip of the Red Giant Branch stars , namely ( m - M ) _ { 0 ,TRGB } ^ { LMC } =18.69 \pm 0.25 \pm 0.06 mag ( statistical plus systematic error ) . Both values agree well with the distance to the SN 1987A as determined from a study of its inner ring fluorescent echo ( ( m - M ) _ { SN~ { } 1987 A } =18.55 \pm 0.05 mag , Panagia 1998 ) , thus excluding distance moduli lower than 18.43 to a 99.7 % significance level . Differences with respect to previous results obtained using the same distance indicators are discussed .