The successive displacements are 5.5 m to the north, 9.3 m northeast, and 4.8 m 54 degrees west of south.
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Without needing to use trigonometry, the north and east components of the 2nd. leg are both (9.3/sqrt.2) = 6.576 metres.
(90 - 53) = 36 deg. south of west.
South component of 3rd. leg = (sin 36) x 4.8 = 2.82 metres.
West component = (cos 36) x 4.8 = 3.88 metres.
Total North = (5.5 + 6.576) - 2.82 = 9.256 metres.
Total East = (6.576 - 3.88) = 2.696 metres.
Displacement from origin = sqrt.(2.696^2 + 9.256^2) = 9.64 metres.
Angle of displacement = arctan (2.696/9.256) = 16.24 degrees East of North.
(90 - 53) = 36 deg. south of west.
South component of 3rd. leg = (sin 36) x 4.8 = 2.82 metres.
West component = (cos 36) x 4.8 = 3.88 metres.
Total North = (5.5 + 6.576) - 2.82 = 9.256 metres.
Total East = (6.576 - 3.88) = 2.696 metres.
Displacement from origin = sqrt.(2.696^2 + 9.256^2) = 9.64 metres.
Angle of displacement = arctan (2.696/9.256) = 16.24 degrees East of North.