5．（a）The sides of the triangle \(A B C\) have lengths \(B C = a , A C = b\) and \(A B = c\) ，where \(a < b < c\) ．The sizes of the angles \(A , B\) and \(C\) form an arithmetic sequence．
（i）Show that the area of triangle \(A B C\) is \(a c \frac { \sqrt { 3 } } { 4 }\) ． Given that \(a = 2\) and \(\sin A = \frac { \sqrt { } 15 } { 5 }\) ，find
（ii）the value of \(b\) ，
（iii）the value of \(c\) ．
（b）The internal angles of an \(n\)－sided polygon form an arithmetic sequence with first term \(143 ^ { \circ }\) and common difference \(2 ^ { \circ }\) ． Given that all of the internal angles are less than \(180 ^ { \circ }\) ，find the value of \(n\) ．