B757 FLT CREW HAS A FLAP MALFUNCTION DURING APCH TO LNDG. DECLARES AN EMER AND PERFORMS CHKLIST ITEMS. LNDG UNEVENTFUL.

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WE WERE AT 3000 FT; CLRED FOR A VISUAL APCH TO RWY 27L ZZZ; FLAPS 15 DEGS; SPD 170 KTS ASSIGNED. WE SELECTED GEAR DOWN F20. THE FLAPS LOCKED AT 17 DEGS AND TRIGGERED A TRAILING EDGE FLAP ASYMMETRY EICAS MESSAGE. WE ADVISED TWR OF OUR NEED TO ABANDON THE APCH AND BREAK OUT OF THE PATTERN TO RUN CHKLISTS. WE CLBED TO 4000 FT HEADING S; AWAY FROM THE ARPT; BROUGHT THE GEAR UP AND AFTER ASSURING SAFE TERRAIN CLRNC AND DISCUSSING FUEL STATUS (7.1 LBS); I RAN THE IRREGULAR CHKLIST WHILE THE FO FLEW THE ACFT AND WORKED THE RADIOS. I ADVISED DISPATCH VIA ACARS WE WERE WORKING ON A FLAP IRREGULARITY AND MADE A PA ANNOUNCEMENT TO THE PAX. THE FLT ATTENDANTS WERE GIVEN A CABIN ADVISORY. THE TRAILING EDGE FLAP ASYMMETRY CHKLIST HAS SEVERAL DECISION POINTS AND CAN BE CONFUSING SO AFTER SEVERAL MINS WE SUCCESSFULLY CONFIGURED THE FLAPS TO 20 DEGS USING THE ALTERNATE SYS; PER THE CHKLIST. ANOTHER FEW MINS LATER WE WERE PREPARED FOR LNDG. DUE TO OUR FUEL BURN RATE WITH FLAPS EXTENDED (8.4 PPH) WITH 5.9 REMAINING AND OUR UNCERTAIN SEQUENCE; I ELECTED TO DECLARE AN EMER TO ENSURE OUR ABILITY TO SAFELY LAND BEFORE OUR FUEL STATE BECAME CRITICAL. WE WERE IMMEDIATELY GIVEN DIRECT ZZZ RWY 32L AND PROCEEDED TO THE ARPT. I ASSUMED CTL OF THE ACFT AND MADE A VISUAL APCH TO RWY 32L WITH A CLOSE-IN L BASE. AS WE TURNED A 2 MI FINAL WE HAD A LOW FUEL EICAS MESSAGE. FUEL WAS INDICATING 3.1/2.1 IN EACH TANK. WE LANDED AND TAXIED TO THE GATE WITHOUT FURTHER INCIDENT. THE EMER WAS DECLARED; NOT BECAUSE OF THE FLAP PROB; BUT DUE TO MY CONCERN FOR THE SAFE OUTCOME OF THE FLT HAD WE TRIED TO FIT INTO THE NORMAL LNDG FLOW.