Please Check.

1) Product  of a complex  number  and a  real  number  is just a scalar of the complex number

3.   a  = 8      c  =11   C  = 33

sin A  /a = sin C/ c

sin A / 8   = sin 33 / 11

sin A  =  (8/11) sin 33

arcsin  [ (8/11) * sin 33 ] = A  = 23.3° 

B =  180  -33  -  23.3   =  123.7°

b/ sin B =  c /sin C

b /  sin 123.7 = 11/sin 33

b =  11 sin 123.7 / sin 33  =   16.8

4.

tan  [ arcsin (-1/2)  ]

________________

cos [ arctan (1)] 

Let  arcsin  (-1/2)  = A      and  arctan (1)  =  B  .....so we  have

tan (A)

______

cos (B)

If arcsin  (-1/2)  = A....rhis  angle  is a Q4  angle....x will  be  positive here

Then   x =  sqrt  [ 4 - 1 ] =   sqrt (3)

So tan (A) =   -1/ sqrt (3)

If  arctan (1)   =  B.......this is a Q1  angle

r=  sqrt  (1 + 1 )   =  sqrt (2)

So  cos B=   1/ sqrt (2)

So we have

(-1/sqrt (3) )  

__________   =

( 1/sqrt (2))

-sqrt (2)  /sqrt (3)   =

- sqrt (6)  / 3

Thank you so much for all your help CPhill! I greatly appreciate your help and time! 😊