A B777 CREW; FOLLOWING A DC10 ON DSCNT; ENCOUNTERED WAKE TURB AT FL366.

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WE WERE DSNDING FROM FL390 THROUGH FL366 WHEN WE HIT WAKE TURB FROM ACR X WHICH WAS 11 MI AHEAD OF US. I LEVELED OFF AND ADDED PWR TO GET ABOVE THEIR DSCNT PROFILE. THE WAKE TURB WAS OVER IN A FEW SECONDS. ATC COULD NOT BELIEVE THAT WE HAD HIT ACR X WAKE TURB; BUT WE DID. FINALLY ATC GAVE ME THE REQUESTED L OR R TURN. THE REST OF THE FLT WAS UNEVENTFUL. AT THE GATE; I ASKED IF ANYONE WAS HURT AND THEN FOUND OUT 1 FLT ATTENDANT HURT HER ANKLE AND CUT A FINGER. NO PAX WERE INJURED. I AM NOT SURE HOW I WILL PREVENT THIS IN THE FUTURE. 11 MI SHOULD BE ENOUGH; BUT IT WASN'T. SUPPLEMENTAL INFO FROM ACN 525933: WE WERE GIVEN A DSCNT CLRNC TO 10000 FT. JUST AFTER WE BEGAN OUR DSCNT; WE ENCOUNTERED WAKE TURB FROM A PRECEDING DC10. MY COPLT WAS FLYING AND TALKING TO ATC WHILE I WAS LISTENING TO ATIS. HE IMMEDIATELY ASKED FOR CLRNC N OR S OF COURSE AND THEN LEVELED OFF. THE ENCOUNTER WAS OVER IN JUST A FEW SECONDS. WE FLEW N OF OUR COURSE ABOUT 2 MI THEN WENT DIRECT TO BAMBO. NO OTHER TURB OCCURRED. AFTER LNDG; WE LEARNED THAT 1 FLT ATTENDANT CUT HER THUMB AND SLIGHTLY TWISTED HER ANKLE DURING THE ENCOUNTER. I DON'T KNOW HER NAME.