By the sine rule
#a/sinA=b/sinB=c/sinC#
Given:
#B=2^@45', b=6.2, c=5.8#
We need to find the angle C immediately
#b/sinB=c/sinC#
#6.2/sin2^@45'=5.8/sinC#
Since the angles are small, #<5^@'#, #sintheta=theta#
when theta is expressed in radians
#2^@45'=2^@+(45/60)^@=2.75^@#
#2.75^@=pi/180xx2.75^@=0.048#
Thus, #sin2^@45'=sin0.05rad=0.048#
and
Thus, #6.2/0.048=5.8/sinC#
#sinC=5.8xx0.048/6.2=0.047#
#C=0.047rad=0.047xx180/pi=2.68^@#
#0.68^@=0.68xx60 min=41'#
hence, #C=2^@41'#
To find a
#sinA=sin(B+C)# by allied angles
#sin(B+C)=sin(2^@45'+2^@41')=sin5.433#
#sinA=sin0.095rad=0.095#
#a/sinA=b/sinB#
#a/0.095=6.2/sin2^@45'=6.2/sin0.048#
#a=602xx0.095/0.048=12.271#
#A+B+C=180#
#A+2^@45'+2^@41'=180#
#A=174^@34'#
Thus, the solution is
#a=12.271, b=6.2, c=5.8# form the sides, while
#A=174^@34', B=2^@45', C=2^@41'# form the angles
