Question 390447
By the law of sines,


{{{a/(sin A) = b/(sin B)}}}


Note that sin A = sin 60 = {{{sqrt(3)/2}}} and sin B = sin 45 = {{{sqrt(2)/2}}}. Replacing all the known values in,


{{{a/(sqrt(3)/2) = 6/(sqrt(2)/2)}}} Cross multiply:


{{{a*sqrt(2)/2 = 6sqrt(3)/2 = 3sqrt(3)}}}


{{{a = 6*sqrt(3)/sqrt(2) = 3sqrt(6)}}}