Area of Triangles

I think hectictar answered something like this a few days ago.....mine isn't as exquisite as hers

Area  =  (1/2)  (a) (b) sin C       (1)

And

   a            b                              a sin B

____  =  ____      so   b  =      ______           (2)

sinA       sin B                            sin A

Sub (2) into (1)     and we have that

Area  =  (1/2) (a) (a sin B) sin C             a^2 sin B sin C

             ___________________    =     ______________

                           ( sin  A)                             2  sin  A

You should be able to do the other two  using

Area =  (1/2) (b) (c) sin A           and   noting that          c  = b sin C /sin B

And

Area  = (1/2) (a) (c) sin B              and noting that   a  = c sin A / sin C