Use the law of cosines to solve for the length of side b. show all of your work for full credit.

According to the law of cosines:

.

Substituting all the values we know and finding  using a calculator, we have:



We discard the negative solution clearly.

b=9 units

The law of cosines states that: 
c² = a² + b² - 2ab*cos(C)
In this case, a and b are the legs we know the length of, and C is the degree opposite the unknown leg, or 33°
Plugging in:
c² = 11² + 16² - 2(11)(16)(cos(33°)
c² = 121 + 256 - 352 (.83)
c² = 81.78
c = 9

The length of side b is about 9