Case I is a statically determinate system, you can get the Vertical force on support "S" by sum moments about support "A", which shall equate to zero.
Case II is statically indeterminate to the first degree. You shall conveniently release the horizontal restrain at support "S", which then becomes identical to case I. Then you have to calculate the horizontal displacement of support point "S" (d1), and apply an unit horizontal force at "S" to get an unit displacement (d2). Now you can get a new set of reactions by equating and proportioning d1 and d2 (sum displacement = 0). Finally, the reactions at supports "A" and "S" can be obtained by superposition using the two sets results. You shall review the structural analysis textbook on "solving structurally indeterminate structures by displacement method".