A B757-200'S RT HYDRAULIC QTY DECREASED IN FLT. SYSTEM SECURED UNTIL LNDG CHK LIST. AN EMER WAS DECLARED FOLLOWED BY A DIVERSION TO A NEARBY ARPT.

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ENRTE TO ZZZ TO ZZZ1 EXPERIENCED LOSS OF R HYD QUANTITY AT CRUISE FL390/MACH .80 AND APPROX 120 NM SW OF XXXXX INTXN. RECEIVED R HYD QUANTITY CAUTION ACCOMPANIED BY R RESERVOIR LIGHT ON HYD OVERHEAD PANEL. R SYS PRESSURE OBSERVED AS NORMAL AND QUANTITY INDICATED .52 MACH WITH RF ILLUMINATED. STABILIZED SYS AS PER QRH PROC AND TURNED OFF R ENG AND ELECTRIC HYD PUMPS. NOTIFIED ATC AND REQUESTED DIVERT DIRECT ZZZ2 WHICH WAS DEEMED AS BEST SUITABLE ALTERNATE 35 MINS AWAY USING NORMAL DSCNT PROCS. NOTIFIED DISPATCH. DECLARED EMER WITH ATC. COORDINATED WITH FLT ATTENDANTS FOR EMER LNDG PREPARATION AND BRIEFING OF PAX. PRIORITY HANDLING RECEIVED WITH ATC VECTORS TO UNEVENTFUL ILS RWY 9 LNDG. AS PER QRH RECOMMENDATION; RESTORED R HYD ELECTRIC PUMP AT 1000 FT AGL FOR STABILITY AND BRAKING. R SYS QUANTITY DECREASED TO .42 MACH AND NORMAL PRESSURE WAS OBSERVED THROUGHOUT LNDG ROLLOUT. STOPPED AND SHUTDOWN ACFT ON RWY AND HAD ARFF CAPT INSPECT BRAKES AND RECEIVED ALL CLR. STAYED ON RWY FOR MAINT TOW TO GATE.