Laws of Sines, need MORE help

Generally got the idea of cosines from my last posted question, now here's a problem with sines:
Given a triangle with a = 150, angle A = 75, and angle C = 30, using the law of sines, what is c?

sin(75)/150=sin(30)/c
c=150*sin(30)/sin(75)

c=77.6457

The Law of Sines states that: a/sin(angleA) = c/sin(angleC). Plug in your values (150)/(sin75) = (c)/(sin30). Cross multiply, giving you 150sin30 = csin75. Divide both sides by sin75 to give you c = 150sin30/sin75, or c = 77.646. Make sure your calculator is set to radian mode before you get your answer.

Edit: I am an idiot. Since everything is in degrees, set your calculator mode to DEGREES, not radians. LOL FAIL.

For triangle with sides a,b, and c and angles A, B and C where
A is opposite to a, B is opposite to b and C is opposite to c
you can say

   a             b            c
--------  =  --------  =  --------
sin(A)      sin(B)     sin(C)

so

  150             c
---------   =  ---------
sin(75)      sin(30)

or

150∙sin(30)
----------------   =  c ≈ 77.64
   sin(75)

sin(A)/a = sin(C)/c
c = a*sin(C)/sin(A)
c = 150*sin(30)/sin(75)
c = (150 * 1/2)/((√6 + √2)/4)
c = 4(75)/(√6 + √2)
c = 300/(√6 + √2)
c = 300(√6 - √2)/(√6 + √2)(√6 - √2)
c = (300√6 - 300√2)/(6 - 2)
c = 75√6 - 75√2