What was found
20 MINUTES INTO CRUISE AT FL380 PIC NOTICED A LOW HYDRAULIC PRESSURE AMBER LIGHT ON THE ANNUNCIATOR. A QUICK LOOK AT THE HYDRAULIC PRESSURE GAUGE SHOWED ZERO PRESSURE IN THE HYDRAULIC SYSTEM. PIC AND FO TOOK OUT THE QRH AND FOLLOWED THE APPROPRIATE CHECKLIST. THESE INCLUDED LO HYD PRESS LIGHT CHECKLIST, HYDRAULIC SYSTEM FAILURE/ALTERNATE GEAR EXTENSION CHECKLIST, AND HYDRAULIC SYSTEM FAILURE LANDING CHECKLIST WHILE CRUISING TO KAPA. DISCUSSED PLAN FOR HOLDING, TALKING WITH OPS AND INSTRUCTOR PILOT AT IJA TO ENSURE NOTHING WAS MISSED. DENVER ATC ELECTED TO JUST GIVE VECTORS RATHER THAN HOLDING. CHECKED WEATHER AT APA AND COMPLETED TOLD INFORMATION. 12 DEGREES CELSIUS, LIGHT WINDS, CLEAR SKIES AND LONG, DRY RUNWAY. LOWERED GEAR WITH ALTERNATE EXTENSION, FLEW A NO FLAP APPROACH AT VREF+20 PER CHECKLIST, LANDED, USED REVERSE THRUST AND THEN IT WAS NECESSARY TO USE EMERGENCY BRAKING TO CLEAR RUNWAY AND ENTER RAMP. ALTHOUGH WE DIDN'T EXPECT TO NEED FIRE TRUCKS, WE FELT IT WAS PRUDENT TO HAVE THEM STANDING BY JUST IN CASE OF ANY UNKNOWNS. AIRCRAFT PARKED AND TURNED OVER TO MAINTENANCE.